{"id":584,"date":"2026-09-24T09:00:00","date_gmt":"2026-09-24T09:00:00","guid":{"rendered":"https:\/\/otus.ru\/journal\/?p=584"},"modified":"2026-09-24T13:00:42","modified_gmt":"2026-09-24T13:00:42","slug":"mera-i-veroyatnost","status":"publish","type":"post","link":"https:\/\/otus.ru\/journal\/mera-i-veroyatnost\/","title":{"rendered":"\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430: \u0430\u043a\u0441\u0438\u043e\u043c\u044b \u041a\u043e\u043b\u043c\u043e\u0433\u043e\u0440\u043e\u0432\u0430 \u0438 \u043f\u0440\u0438\u043c\u0435\u0440 \u0441 \u043c\u0438\u0448\u0435\u043d\u044c\u044e"},"content":{"rendered":"<p><strong>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430<\/strong> &#8212; \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f P, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043a\u0430\u0436\u0434\u043e\u043c\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044e A \u0438\u0437 \u0437\u0430\u0440\u0430\u043d\u0435\u0435 \u0432\u044b\u0431\u0440\u0430\u043d\u043d\u043e\u0433\u043e \u0441\u0435\u043c\u0435\u0439\u0441\u0442\u0432\u0430 \u0441\u043e\u0431\u044b\u0442\u0438\u0439 F \u0441\u0442\u0430\u0432\u0438\u0442 \u0432 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0435 \u0447\u0438\u0441\u043b\u043e P(A) \u043e\u0442 0 \u0434\u043e 1 \u0442\u0430\u043a, \u0447\u0442\u043e P(\u03a9) = 1 \u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u044f \u043f\u043e\u043f\u0430\u0440\u043d\u043e \u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0440\u0430\u0432\u043d\u0430 \u0441\u0443\u043c\u043c\u0435 \u0438\u0445 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439. \u0418\u043d\u0430\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u044d\u0442\u043e \u043c\u0435\u0440\u0430 \u0441 \u043f\u043e\u043b\u043d\u043e\u0439 \u043c\u0430\u0441\u0441\u043e\u0439 1. \u0412\u043c\u0435\u0441\u0442\u0435 \u0441 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e\u043c \u0438\u0441\u0445\u043e\u0434\u043e\u0432 \u03a9 \u0438 \u0441\u0435\u043c\u0435\u0439\u0441\u0442\u0432\u043e\u043c \u0441\u043e\u0431\u044b\u0442\u0438\u0439 F \u043e\u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u0443\u0435\u0442 <strong>\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e<\/strong> (\u03a9, F, P).<\/p>\n<div class=\"oj-toc\" style=\"background:#f6f6f6;border-radius:8px;padding:14px 20px;margin:20px 0\">\n<p><strong>\u0421\u043e\u0434\u0435\u0440\u0436\u0430\u043d\u0438\u0435<\/strong><\/p>\n<ol>\n<li><a href=\"#s1\">\u041c\u0438\u043d\u0438-\u0441\u043b\u043e\u0432\u0430\u0440\u044c: \u0447\u0435\u0442\u044b\u0440\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0443\u0442\u0430\u044e\u0442<\/a><\/li>\n<li><a href=\"#s2\">\u0410\u043a\u0441\u0438\u043e\u043c\u044b \u041a\u043e\u043b\u043c\u043e\u0433\u043e\u0440\u043e\u0432\u0430<\/a><\/li>\n<li><a href=\"#s3\">\u041c\u0435\u0440\u0430, \u043c\u0435\u0440\u0430 \u041b\u0435\u0431\u0435\u0433\u0430 \u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430<\/a><\/li>\n<li><a href=\"#s4\">\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c: \u043c\u0438\u0448\u0435\u043d\u044c<\/a><\/li>\n<li><a href=\"#s5\">\u0412\u044b\u0432\u043e\u0434\u044b<\/a><\/li>\n<li><a href=\"#s6\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/a><\/li>\n<li><a href=\"#s7\">FAQ<\/a><\/li>\n<\/ol>\n<\/div>\n<p>\u041d\u0438\u0436\u0435 &#8212; \u043c\u0438\u043d\u0438-\u0441\u043b\u043e\u0432\u0430\u0440\u044c, \u0442\u0440\u0438 \u0430\u043a\u0441\u0438\u043e\u043c\u044b \u041a\u043e\u043b\u043c\u043e\u0433\u043e\u0440\u043e\u0432\u0430 \u0438 \u0438\u0445 \u0441\u043b\u0435\u0434\u0441\u0442\u0432\u0438\u044f, \u0447\u0435\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430 \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u043c\u0435\u0440\u044b \u041b\u0435\u0431\u0435\u0433\u0430, \u0438 \u0440\u0430\u0437\u0431\u043e\u0440 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u043d\u0430 \u043c\u0438\u0448\u0435\u043d\u0438 \u0441 \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u043e\u0439 \u0432 Python.<\/p>\n<h2 id=\"s1\">\u041c\u0438\u043d\u0438-\u0441\u043b\u043e\u0432\u0430\u0440\u044c: \u0447\u0435\u0442\u044b\u0440\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0443\u0442\u0430\u044e\u0442<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u0422\u0435\u0440\u043c\u0438\u043d<\/th>\n<th>\u0427\u0442\u043e \u044d\u0442\u043e<\/th>\n<th>\u041f\u0440\u0438\u043c\u0435\u0440 \u0434\u043b\u044f \u043a\u0443\u0431\u0438\u043a\u0430<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u03a9 &#8212; \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u044b\u0445 \u0438\u0441\u0445\u043e\u0434\u043e\u0432<\/td>\n<td>\u041c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0432\u0441\u0435\u0445 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0445 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432 \u043e\u043f\u044b\u0442\u0430<\/td>\n<td>{1, 2, 3, 4, 5, 6}<\/td>\n<\/tr>\n<tr>\n<td>\u0421\u043e\u0431\u044b\u0442\u0438\u0435<\/td>\n<td>\u041f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u03a9, \u043a\u043e\u0442\u043e\u0440\u043e\u043c\u0443 \u043c\u043e\u0434\u0435\u043b\u044c \u043f\u0440\u0438\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c<\/td>\n<td>\u00ab\u0432\u044b\u043f\u0430\u043b\u043e \u0447\u0435\u0442\u043d\u043e\u0435\u00bb = {2, 4, 6}<\/td>\n<\/tr>\n<tr>\n<td>F &#8212; \u0441\u0438\u0433\u043c\u0430-\u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0441\u043e\u0431\u044b\u0442\u0438\u0439<\/td>\n<td>\u0421\u0435\u043c\u0435\u0439\u0441\u0442\u0432\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u0439: \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u03a9, \u0437\u0430\u043c\u043a\u043d\u0443\u0442\u043e \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u0438 \u0441\u0447\u0435\u0442\u043d\u043e\u0433\u043e \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u044f<\/td>\n<td>\u0412\u0441\u0435 64 \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u03a9<\/td>\n<\/tr>\n<tr>\n<td>P &#8212; \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430<\/td>\n<td>\u0424\u0443\u043d\u043a\u0446\u0438\u044f F -&gt; [0, 1], \u043f\u043e\u0434\u0447\u0438\u043d\u0435\u043d\u043d\u0430\u044f \u0430\u043a\u0441\u0438\u043e\u043c\u0430\u043c<\/td>\n<td>P(A) = \u0447\u0438\u0441\u043b\u043e \u0433\u0440\u0430\u043d\u0435\u0439 \u0432 A \/ 6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0413\u043b\u0430\u0432\u043d\u043e\u0435 \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u0435: \u0438\u0441\u0445\u043e\u0434 &#8212; \u044d\u0442\u043e \u0442\u043e\u0447\u043a\u0430 \u03a9, \u0430 \u0441\u043e\u0431\u044b\u0442\u0438\u0435 &#8212; \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0438\u0441\u0445\u043e\u0434\u043e\u0432. \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043f\u0440\u0438\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c, \u0430 \u043d\u0435 \u0438\u0441\u0445\u043e\u0434\u0430\u043c \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e.<\/p>\n<h2 id=\"s2\">\u0410\u043a\u0441\u0438\u043e\u043c\u044b \u041a\u043e\u043b\u043c\u043e\u0433\u043e\u0440\u043e\u0432\u0430<\/h2>\n<p>\u0410\u043a\u0441\u0438\u043e\u043c\u0430\u0442\u0438\u043a\u0443 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0438\u043b \u0410. \u041d. \u041a\u043e\u043b\u043c\u043e\u0433\u043e\u0440\u043e\u0432 \u0432 1933 \u0433\u043e\u0434\u0443 \u0432 \u043a\u043d\u0438\u0433\u0435 \u043d\u0430 \u043d\u0435\u043c\u0435\u0446\u043a\u043e\u043c \u044f\u0437\u044b\u043a\u0435 \u00abGrundbegriffe der Wahrscheinlichkeitsrechnung\u00bb; \u0440\u0443\u0441\u0441\u043a\u043e\u0435 \u0438\u0437\u0434\u0430\u043d\u0438\u0435 \u0432\u044b\u0448\u043b\u043e \u0432 1936 \u0433\u043e\u0434\u0443 \u043f\u043e\u0434 \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u0435\u043c \u00ab\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0442\u0435\u043e\u0440\u0438\u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439\u00bb. \u0424\u0443\u043d\u043a\u0446\u0438\u044f P: F -&gt; \u211d \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u043e\u0439 \u043c\u0435\u0440\u043e\u0439, \u0435\u0441\u043b\u0438:<\/p>\n<ol>\n<li><strong>\u041d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c:<\/strong> P(A) \u2265 0 \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u044f A \u0438\u0437 F.<\/li>\n<li><strong>\u041d\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u043a\u0430:<\/strong> P(\u03a9) = 1.<\/li>\n<li><strong>\u0421\u0447\u0435\u0442\u043d\u0430\u044f \u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c:<\/strong> \u0435\u0441\u043b\u0438 \u0441\u043e\u0431\u044b\u0442\u0438\u044f A\u2081, A\u2082, &#8230; \u043f\u043e\u043f\u0430\u0440\u043d\u043e \u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b (A\u1d62 \u2229 A\u2c7c = \u2205 \u043f\u0440\u0438 i \u2260 j), \u0442\u043e P(A\u2081 \u222a A\u2082 \u222a &#8230;) = P(A\u2081) + P(A\u2082) + &#8230;<\/li>\n<\/ol>\n<p>\u0412\u0430\u0436\u043d\u0430\u044f \u043e\u0433\u043e\u0432\u043e\u0440\u043a\u0430 \u043a \u0442\u0440\u0435\u0442\u044c\u0435\u0439 \u0430\u043a\u0441\u0438\u043e\u043c\u0435: \u043e\u043d\u0430 \u043f\u0440\u043e <strong>\u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b\u0435<\/strong> \u0441\u043e\u0431\u044b\u0442\u0438\u044f (\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0442\u0441\u044f), \u0430 \u043d\u0435 \u043f\u0440\u043e <strong>\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435<\/strong>. \u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c &#8212; \u0434\u0440\u0443\u0433\u043e\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e: P(A \u2229 B) = P(A) \u00b7 P(B). \u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0441\u043e\u0431\u044b\u0442\u0438\u044f \u0441 \u043d\u0435\u043d\u0443\u043b\u0435\u0432\u044b\u043c\u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044f\u043c\u0438 \u043a\u0430\u043a \u0440\u0430\u0437 \u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b, \u0438 \u0441\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u0442\u044c \u0438\u0445 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u043d\u0435\u043b\u044c\u0437\u044f.<\/p>\n<h3>\u0427\u0442\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0438\u0437 \u0430\u043a\u0441\u0438\u043e\u043c<\/h3>\n<p>\u041e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0440\u0438\u0432\u044b\u0447\u043d\u044b\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0432\u044b\u0432\u043e\u0434\u044f\u0442\u0441\u044f, \u0430 \u043d\u0435 \u043f\u043e\u0441\u0442\u0443\u043b\u0438\u0440\u0443\u044e\u0442\u0441\u044f:<\/p>\n<ul>\n<li>P(\u2205) = 0;<\/li>\n<li>P(\u043d\u0435 A) = 1 &#8212; P(A);<\/li>\n<li>\u0435\u0441\u043b\u0438 A \u2282 B, \u0442\u043e P(A) \u2264 P(B), \u043f\u043e\u044d\u0442\u043e\u043c\u0443 P(A) \u2264 1 \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e A;<\/li>\n<li>P(A \u222a B) = P(A) + P(B) &#8212; P(A \u2229 B) \u0434\u043b\u044f \u043b\u044e\u0431\u044b\u0445, \u0432 \u0442\u043e\u043c \u0447\u0438\u0441\u043b\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0445\u0441\u044f, \u0441\u043e\u0431\u044b\u0442\u0438\u0439;<\/li>\n<li>\u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c: \u0435\u0441\u043b\u0438 A\u2081 \u2282 A\u2082 \u2282 &#8230;, \u0442\u043e P(A\u2099) \u0441\u0442\u0440\u0435\u043c\u0438\u0442\u0441\u044f \u043a P(\u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u044f).<\/li>\n<\/ul>\n<h3>\u041f\u0440\u043e\u0432\u0435\u0440\u043a\u0430 \u043d\u0430 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435<\/h3>\n<p>\u0414\u043b\u044f \u043a\u0443\u0431\u0438\u043a\u0430 \u0432\u0441\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u043f\u0435\u0440\u0435\u0431\u0440\u0430\u0442\u044c \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e: \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0432\u0441\u0435\u0433\u043e 2\u2076 = 64. \u041a\u043e\u0434 \u0441\u0447\u0438\u0442\u0430\u0435\u0442 \u0442\u043e\u0447\u043d\u043e, \u043d\u0430 \u0434\u0440\u043e\u0431\u044f\u0445, \u0431\u0435\u0437 \u043e\u0448\u0438\u0431\u043e\u043a \u043e\u043a\u0440\u0443\u0433\u043b\u0435\u043d\u0438\u044f.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">fractions<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">Fraction<\/span>\n<span style=\"color: #C678DD\">from<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">itertools<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #C678DD\">import<\/span> <span style=\"color: #E06C75\">chain<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">combinations<\/span>\n\n<span style=\"color: #E06C75\">omega<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">frozenset<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">7<\/span><span style=\"color: #ABB2BF\">))<\/span>            <span style=\"color: #7F848E\"># \u0433\u0440\u0430\u043d\u0438 \u043a\u0443\u0431\u0438\u043a\u0430<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">event<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #C678DD\">assert<\/span> <span style=\"color: #E06C75\">event<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #E06C75\">omega<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #98C379\">\"\u0441\u043e\u0431\u044b\u0442\u0438\u0435 \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e\u043c omega\"<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">Fraction<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">event<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">omega<\/span><span style=\"color: #ABB2BF\">))<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">all_events<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">s<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">items<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">list<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">s<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #ABB2BF\">[<\/span><span style=\"color: #E5C07B\">frozenset<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">c<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">c<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">chain<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">from_iterable<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">combinations<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">items<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">k<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">k<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">items<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\">))]<\/span>\n\n<span style=\"color: #E06C75\">F<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">all_events<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">omega<\/span><span style=\"color: #ABB2BF\">)<\/span>                     <span style=\"color: #7F848E\"># \u0441\u0438\u0433\u043c\u0430-\u0430\u043b\u0433\u0435\u0431\u0440\u0430 = \u0432\u0441\u0435 2^6 \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0432 F:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">len<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">F<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"P(omega) =\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">omega<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #98C379\">\"| P(\u043f\u0443\u0441\u0442\u043e\u0435) =\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E5C07B\">frozenset<\/span><span style=\"color: #ABB2BF\">()))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u0432\u0441\u0435 P \u0432 [0, 1]:\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E5C07B\">all<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">A<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #D19A66\">1<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">A<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">F<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"\u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c \u0434\u043b\u044f \u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b\u0445:\"<\/span><span style=\"color: #ABB2BF\">,<\/span>\n      <span style=\"color: #E5C07B\">all<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">A<\/span> <span style=\"color: #56B6C2\">|<\/span> <span style=\"color: #E06C75\">B<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">==<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">A<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">B<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">A<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">F<\/span> <span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">B<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E06C75\">F<\/span> <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #56B6C2\">not<\/span> <span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">A<\/span> <span style=\"color: #56B6C2\">&amp;<\/span> <span style=\"color: #E06C75\">B<\/span><span style=\"color: #ABB2BF\">)))<\/span>\n\n<span style=\"color: #E06C75\">even<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">big<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E5C07B\">frozenset<\/span><span style=\"color: #ABB2BF\">({<\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">4<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">6<\/span><span style=\"color: #ABB2BF\">}),<\/span> <span style=\"color: #E5C07B\">frozenset<\/span><span style=\"color: #ABB2BF\">({<\/span><span style=\"color: #D19A66\">4<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">5<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">6<\/span><span style=\"color: #ABB2BF\">})<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"P(\u0447\u0435\u0442) + P(&gt;=4) =\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">even<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">big<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #98C379\">\"| P(\u0447\u0435\u0442 \u0438\u043b\u0438 &gt;=4) =\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">even<\/span> <span style=\"color: #56B6C2\">|<\/span> <span style=\"color: #E06C75\">big<\/span><span style=\"color: #ABB2BF\">))<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">\"P(A) + P(B) - P(AB) =\"<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">even<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">big<\/span><span style=\"color: #ABB2BF\">)<\/span> <span style=\"color: #56B6C2\">-<\/span> <span style=\"color: #E06C75\">P<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">even<\/span> <span style=\"color: #56B6C2\">&amp;<\/span> <span style=\"color: #E06C75\">big<\/span><span style=\"color: #ABB2BF\">))<\/span><\/code><\/pre>\n<p>\u0412\u044b\u0432\u043e\u0434 (Python 3.14.7):<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">\u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0432 F: 64\nP(omega) = 1 | P(\u043f\u0443\u0441\u0442\u043e\u0435) = 0\n\u0432\u0441\u0435 P \u0432 [0, 1]: True\n\u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c \u0434\u043b\u044f \u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b\u0445: True\nP(\u0447\u0435\u0442) + P(&gt;=4) = 1 | P(\u0447\u0435\u0442 \u0438\u043b\u0438 &gt;=4) = 2\/3\nP(A) + P(B) - P(AB) = 2\/3\n<\/code><\/pre>\n<p>\u041f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0435 \u0434\u0432\u0435 \u0441\u0442\u0440\u043e\u043a\u0438 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u043e\u0448\u0438\u0431\u043a\u0443 \u00ab\u0441\u043b\u043e\u0436\u0438\u0442\u044c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0445\u0441\u044f \u0441\u043e\u0431\u044b\u0442\u0438\u0439\u00bb: \u0441\u0443\u043c\u043c\u0430 \u0434\u0430\u0435\u0442 1, \u0430 \u0432\u0435\u0440\u043d\u044b\u0439 \u043e\u0442\u0432\u0435\u0442 2\/3, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0438\u0441\u0445\u043e\u0434\u044b 4 \u0438 6 \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u043d\u044b \u0434\u0432\u0430\u0436\u0434\u044b. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0441 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435\u043c P(A \u2229 B) \u044d\u0442\u043e \u0438\u0441\u043f\u0440\u0430\u0432\u043b\u044f\u0435\u0442. \u0414\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u03a9 \u0441\u0447\u0435\u0442\u043d\u0430\u044f \u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c \u0441\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043a \u043f\u043e\u043f\u0430\u0440\u043d\u043e\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0442\u0430\u043a\u043e\u0439 \u043f\u0435\u0440\u0435\u0431\u043e\u0440 &#8212; \u043f\u043e\u043b\u043d\u0430\u044f \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0430.<\/p>\n<h2 id=\"s3\">\u041c\u0435\u0440\u0430, \u043c\u0435\u0440\u0430 \u041b\u0435\u0431\u0435\u0433\u0430 \u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430<\/h2>\n<p>\u0421\u043b\u043e\u0432\u043e \u00ab\u043c\u0435\u0440\u0430\u00bb \u0432 \u043d\u0430\u0437\u0432\u0430\u043d\u0438\u0438 \u043d\u0435 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e: \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c &#8212; \u0447\u0430\u0441\u0442\u043d\u044b\u0439 \u0441\u043b\u0443\u0447\u0430\u0439 \u043e\u0431\u0449\u0435\u0433\u043e \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u043c\u0435\u0440\u044b \u0438\u0437 \u0430\u043d\u0430\u043b\u0438\u0437\u0430.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u041f\u043e\u043d\u044f\u0442\u0438\u0435<\/th>\n<th>\u0417\u043d\u0430\u0447\u0435\u043d\u0438\u044f<\/th>\n<th>\u041f\u043e\u043b\u043d\u0430\u044f \u043c\u0430\u0441\u0441\u0430<\/th>\n<th>\u041f\u0440\u0438\u043c\u0435\u0440<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u041c\u0435\u0440\u0430<\/td>\n<td>[0, +\u221e]<\/td>\n<td>\u041b\u044e\u0431\u0430\u044f, \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0439<\/td>\n<td>\u0427\u0438\u0441\u043b\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430<\/td>\n<\/tr>\n<tr>\n<td>\u041c\u0435\u0440\u0430 \u041b\u0435\u0431\u0435\u0433\u0430 \u03bb<\/td>\n<td>[0, +\u221e]<\/td>\n<td>\u041d\u0430 \u0432\u0441\u0435\u0439 \u043f\u0440\u044f\u043c\u043e\u0439 \u0438\u043b\u0438 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u0430<\/td>\n<td>\u0414\u043b\u0438\u043d\u0430, \u043f\u043b\u043e\u0449\u0430\u0434\u044c, \u043e\u0431\u044a\u0435\u043c<\/td>\n<\/tr>\n<tr>\n<td>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430 P<\/td>\n<td>[0, 1]<\/td>\n<td>\u0420\u043e\u0432\u043d\u043e 1<\/td>\n<td>\u0420\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u043a\u0440\u0443\u0433\u0435<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u041c\u0435\u0440\u0430 \u041b\u0435\u0431\u0435\u0433\u0430 \u043e\u0431\u043e\u0431\u0449\u0430\u0435\u0442 \u0434\u043b\u0438\u043d\u0443, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0438 \u043e\u0431\u044a\u0435\u043c, \u043d\u043e \u0441\u0430\u043c\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\u044e \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f: \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0432\u0441\u0435\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u0430. \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f, \u0435\u0441\u043b\u0438 \u0432\u0437\u044f\u0442\u044c \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0443\u044e \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u03a9 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u0438 <strong>\u043d\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u0442\u044c<\/strong>: P(A) = \u03bb(A) \/ \u03bb(\u03a9). \u042d\u0442\u043e \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u03a9, \u0438 \u0442\u043e\u043b\u044c\u043a\u043e \u043e\u043d\u043e. \u0414\u0440\u0443\u0433\u0438\u0435 \u043c\u043e\u0434\u0435\u043b\u0438 \u0437\u0430\u0434\u0430\u044e\u0442\u0441\u044f \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043c\u0435\u0440\u0430\u043c\u0438, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u0447\u0435\u0440\u0435\u0437 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c: P(A) \u0440\u0430\u0432\u043d\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u0443 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u0438 f \u043f\u043e \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0443 A.<\/p>\n<h3>\u0417\u0430\u0447\u0435\u043c \u043d\u0443\u0436\u043d\u0430 \u0441\u0438\u0433\u043c\u0430-\u0430\u043b\u0433\u0435\u0431\u0440\u0430, \u0430 \u043d\u0435 \u0432\u0441\u0435 \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430<\/h3>\n<p>\u0414\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u0441\u0447\u0435\u0442\u043d\u043e\u0433\u043e \u03a9 \u0441\u043e\u0431\u044b\u0442\u0438\u0435\u043c \u043c\u043e\u0436\u043d\u043e \u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043b\u044e\u0431\u043e\u0435 \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e. \u0414\u043b\u044f \u043e\u0442\u0440\u0435\u0437\u043a\u0430 \u0438\u043b\u0438 \u043a\u0440\u0443\u0433\u0430 \u0442\u0430\u043a \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u0441\u044f: \u0432 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0438\u0438 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432 (\u0441 \u0430\u043a\u0441\u0438\u043e\u043c\u043e\u0439 \u0432\u044b\u0431\u043e\u0440\u0430) \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u043d\u0435\u0438\u0437\u043c\u0435\u0440\u0438\u043c\u044b\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0412\u0438\u0442\u0430\u043b\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u043d\u0435\u043b\u044c\u0437\u044f \u0441\u043e\u0433\u043b\u0430\u0441\u043e\u0432\u0430\u043d\u043d\u043e \u043f\u0440\u0438\u043f\u0438\u0441\u0430\u0442\u044c \u0434\u043b\u0438\u043d\u0443. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 F \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0438\u0432\u0430\u044e\u0442 \u0438\u0437\u043c\u0435\u0440\u0438\u043c\u044b\u043c\u0438 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430\u043c\u0438. \u0414\u043b\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u044d\u0442\u043e \u0431\u043e\u0440\u0435\u043b\u0435\u0432\u0441\u043a\u0430\u044f \u0438\u043b\u0438 \u043b\u0435\u0431\u0435\u0433\u043e\u0432\u0430 \u0441\u0438\u0433\u043c\u0430-\u0430\u043b\u0433\u0435\u0431\u0440\u0430 &#8212; \u0432 \u043d\u0435\u0435 \u0432\u0445\u043e\u0434\u044f\u0442 \u0432\u0441\u0435 \u043a\u0440\u0443\u0433\u0438, \u043a\u043e\u043b\u044c\u0446\u0430, \u0441\u0435\u043a\u0442\u043e\u0440\u044b \u0438 \u043b\u044e\u0431\u044b\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435.<\/p>\n<h2 id=\"s4\">\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c: \u043c\u0438\u0448\u0435\u043d\u044c<\/h2>\n<p>\u041f\u043e\u0441\u0442\u0440\u043e\u0438\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u0434\u043b\u044f \u0432\u044b\u0441\u0442\u0440\u0435\u043b\u0430 \u043f\u043e \u043a\u0440\u0443\u0433\u043b\u043e\u0439 \u043c\u0438\u0448\u0435\u043d\u0438 \u0440\u0430\u0434\u0438\u0443\u0441\u0430 R. \u041c\u043e\u0434\u0435\u043b\u044c \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u0430\u044f: \u0441\u0447\u0438\u0442\u0430\u0435\u043c, \u0447\u0442\u043e \u0441\u0442\u0440\u0435\u043b\u043e\u043a \u0432\u0441\u0435\u0433\u0434\u0430 \u043f\u043e\u043f\u0430\u0434\u0430\u0435\u0442 \u0432 \u043c\u0438\u0448\u0435\u043d\u044c \u0438 \u043b\u044e\u0431\u043e\u0435 \u043c\u0435\u0441\u0442\u043e \u0432 \u043d\u0435\u0439 \u0440\u0430\u0432\u043d\u043e\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e.<\/p>\n<ol>\n<li><strong>\u03a9<\/strong> &#8212; \u043a\u0440\u0443\u0433 \u0440\u0430\u0434\u0438\u0443\u0441\u0430 R \u0441 \u0446\u0435\u043d\u0442\u0440\u043e\u043c \u0432 \u043d\u0430\u0447\u0430\u043b\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442.<\/li>\n<li><strong>F<\/strong> &#8212; \u0438\u0437\u043c\u0435\u0440\u0438\u043c\u044b\u0435 (\u043f\u043e \u041b\u0435\u0431\u0435\u0433\u0443) \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430 \u044d\u0442\u043e\u0433\u043e \u043a\u0440\u0443\u0433\u0430.<\/li>\n<li><strong>P(A) = \u03bb\u2082(A) \/ (\u03c0R\u00b2)<\/strong>, \u0433\u0434\u0435 \u03bb\u2082 &#8212; \u043f\u043b\u043e\u0449\u0430\u0434\u044c.<\/li>\n<\/ol>\n<p>\u0410\u043a\u0441\u0438\u043e\u043c\u044b \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u044b: \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430, P(\u03a9) = \u03c0R\u00b2 \/ \u03c0R\u00b2 = 1, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043d\u0435\u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u0445\u0441\u044f \u0444\u0438\u0433\u0443\u0440 \u0441\u043a\u043b\u0430\u0434\u044b\u0432\u0430\u0435\u0442\u0441\u044f. \u00ab\u0414\u0435\u0441\u044f\u0442\u043a\u0430\u00bb &#8212; \u043a\u0440\u0443\u0433 \u0440\u0430\u0434\u0438\u0443\u0441\u0430 r \u0441 \u0442\u0435\u043c \u0436\u0435 \u0446\u0435\u043d\u0442\u0440\u043e\u043c, \u043f\u043e\u044d\u0442\u043e\u043c\u0443:<\/p>\n<p>P(\u00ab\u0434\u0435\u0441\u044f\u0442\u043a\u0430\u00bb) = \u03c0r\u00b2 \/ \u03c0R\u00b2 = (r \/ R)\u00b2<\/p>\n<p>\u041f\u0440\u0438 R = 1 \u0438 r = 0,3 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c 0,09. \u041f\u0440\u043e\u0432\u0435\u0440\u0438\u043c \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u041c\u043e\u043d\u0442\u0435-\u041a\u0430\u0440\u043b\u043e: \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u043c \u043c\u0438\u043b\u043b\u0438\u043e\u043d \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u044b\u0445 \u0442\u043e\u0447\u0435\u043a \u0432 \u043a\u0440\u0443\u0433\u0435 \u0438 \u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0434\u043e\u043b\u044e \u043f\u043e\u043f\u0430\u0432\u0448\u0438\u0445 \u0432 \u00ab\u0434\u0435\u0441\u044f\u0442\u043a\u0443\u00bb.<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">math<\/span>\n<span style=\"color: #C678DD\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">random<\/span>\n\n<span style=\"color: #E06C75\">R<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">r<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">1.0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">0.3<\/span>      <span style=\"color: #7F848E\"># \u0440\u0430\u0434\u0438\u0443\u0441 \u043c\u0438\u0448\u0435\u043d\u0438 \u0438 \u0440\u0430\u0434\u0438\u0443\u0441 \u00ab\u0434\u0435\u0441\u044f\u0442\u043a\u0438\u00bb<\/span>\n<span style=\"color: #E06C75\">N<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">1_000_000<\/span>\n<span style=\"color: #E06C75\">rng<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">Random<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">42<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #C678DD\">def<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #61AFEF; font-weight: bold\">uniform_point_in_disk<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">rng<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">R<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #7F848E\"># \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e \u043f\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u0438: \u0440\u0430\u0434\u0438\u0443\u0441 \u0447\u0435\u0440\u0435\u0437 \u043a\u043e\u0440\u0435\u043d\u044c<\/span>\n    <span style=\"color: #E06C75\">rho<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">R<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">math<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">sqrt<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">rng<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #ABB2BF\">())<\/span>\n    <span style=\"color: #E06C75\">phi<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">2<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">math<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">pi<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">rng<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">random<\/span><span style=\"color: #ABB2BF\">()<\/span>\n    <span style=\"color: #C678DD\">return<\/span> <span style=\"color: #E06C75\">rho<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">math<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">cos<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">phi<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #E06C75\">rho<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">math<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">sin<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">phi<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E06C75\">hits<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">_<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">N<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">x<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">uniform_point_in_disk<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">rng<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">R<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #E06C75\">r<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">r<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">hits<\/span> <span style=\"color: #56B6C2\">+=<\/span> <span style=\"color: #D19A66\">1<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"\u0444\u043e\u0440\u043c\u0443\u043b\u0430 (r\/R)^2 = {<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">r<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">\/<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">R<\/span><span style=\"color: #ABB2BF\">) <\/span><span style=\"color: #56B6C2\">**<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"\u0447\u0430\u0441\u0442\u043e\u0442\u0430 \u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u0439 = {<\/span><span style=\"color: #E06C75\">hits<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">\/<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">N<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">\u0444\u043e\u0440\u043c\u0443\u043b\u0430 (r\/R)^2 = 0.0900\n\u0447\u0430\u0441\u0442\u043e\u0442\u0430 \u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u0439 = 0.0900\n<\/code><\/pre>\n<p>\u0427\u0430\u0441\u0442\u043e\u0442\u0430 \u0441\u043e\u0432\u043f\u0430\u043b\u0430 \u0441 \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u0434\u043e \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u0433\u043e \u0437\u043d\u0430\u043a\u0430. \u042d\u0442\u043e \u043d\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e, \u0430 \u0438\u043b\u043b\u044e\u0441\u0442\u0440\u0430\u0446\u0438\u044f \u0437\u0430\u043a\u043e\u043d\u0430 \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0447\u0438\u0441\u0435\u043b: \u043f\u0440\u0438 \u0434\u0440\u0443\u0433\u043e\u043c seed \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0439 \u0437\u043d\u0430\u043a \u043c\u043e\u0436\u0435\u0442 \u043e\u0442\u043b\u0438\u0447\u0430\u0442\u044c\u0441\u044f.<\/p>\n<h3>\u0422\u0438\u043f\u0438\u0447\u043d\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430: \u00ab\u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u044b\u0439 \u0440\u0430\u0434\u0438\u0443\u0441\u00bb \u043d\u0435 \u0440\u0430\u0432\u0435\u043d \u00ab\u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0439 \u043f\u043b\u043e\u0449\u0430\u0434\u0438\u00bb<\/h3>\n<p>\u0427\u0430\u0441\u0442\u0430\u044f \u043e\u0448\u0438\u0431\u043a\u0430 \u043f\u0440\u0438 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 &#8212; \u0432\u044b\u0431\u0440\u0430\u0442\u044c \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0446\u0435\u043d\u0442\u0440\u0430 \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e: <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">rho = R * rng.random()<\/code>. \u0422\u043e\u0442 \u0436\u0435 \u043a\u043e\u0434 \u0441 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u043e\u043a\u043e\u0439 (seed 42) \u043f\u0435\u0447\u0430\u0442\u0430\u0435\u0442:<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">\u0444\u043e\u0440\u043c\u0443\u043b\u0430 (r\/R)^2 = 0.0900\n\u0447\u0430\u0441\u0442\u043e\u0442\u0430 \u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u0439 = 0.3002\n<\/code><\/pre>\n<p>\u041f\u043e\u043b\u0443\u0447\u0438\u043b\u043e\u0441\u044c \u043e\u043a\u043e\u043b\u043e r \/ R = 0,3, \u0430 \u043d\u0435 0,09. \u041f\u0440\u0438\u0447\u0438\u043d\u0430: \u043a\u043e\u043b\u0435\u0446 \u043c\u0430\u043b\u043e\u0433\u043e \u0440\u0430\u0434\u0438\u0443\u0441\u0430 \u0441\u0442\u043e\u043b\u044c\u043a\u043e \u0436\u0435, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u0445, \u043d\u043e \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0443 \u043d\u0438\u0445 \u043c\u0435\u043d\u044c\u0448\u0435, \u0438 \u0442\u043e\u0447\u043a\u0438 \u0441\u0433\u0443\u0449\u0430\u044e\u0442\u0441\u044f \u043a \u0446\u0435\u043d\u0442\u0440\u0443. \u0422\u0430\u043a\u0430\u044f \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0430 \u0437\u0430\u0434\u0430\u0435\u0442 \u0434\u0440\u0443\u0433\u0443\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0443\u044e \u043c\u0435\u0440\u0443 \u043d\u0430 \u0442\u043e\u043c \u0436\u0435 \u03a9. \u0418\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 &#8212; <code style=\"background:#eef0f3;color:#24292f;border-radius:4px;padding:1px 5px;font-size:0.92em;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\">rho = R * math.sqrt(rng.random())<\/code>: \u0442\u043e\u0433\u0434\u0430 P(\u03c1 \u2264 r) = (r \/ R)\u00b2, \u043a\u0430\u043a \u0438 \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u043f\u043b\u043e\u0449\u0430\u0434\u044c.<\/p>\n<p>\u0412\u044b\u0432\u043e\u0434 \u0448\u0438\u0440\u0435 \u043a\u043e\u0434\u0430: \u0441\u043b\u043e\u0432\u0430 \u00ab\u043d\u0430\u0443\u0434\u0430\u0447\u0443\u00bb \u0438 \u00ab\u0440\u0430\u0432\u043d\u043e\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u00bb \u043d\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u044e\u0442 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0441\u0430\u043c\u0438 \u043f\u043e \u0441\u0435\u0431\u0435. \u041d\u0443\u0436\u043d\u043e \u044f\u0432\u043d\u043e \u0441\u043a\u0430\u0437\u0430\u0442\u044c, \u043a\u0430\u043a\u0430\u044f \u043c\u0435\u0440\u0430 \u0432\u044b\u0431\u0440\u0430\u043d\u0430. \u041d\u0430 \u044d\u0442\u043e\u043c \u043f\u043e\u0441\u0442\u0440\u043e\u0435\u043d \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0439 \u043f\u0430\u0440\u0430\u0434\u043e\u043a\u0441 \u0411\u0435\u0440\u0442\u0440\u0430\u043d\u0430 \u043e \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0439 \u0445\u043e\u0440\u0434\u0435, \u0433\u0434\u0435 \u0442\u0440\u0438 \u00ab\u0435\u0441\u0442\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0445\u00bb \u0441\u043f\u043e\u0441\u043e\u0431\u0430 \u0434\u0430\u044e\u0442 \u0442\u0440\u0438 \u0440\u0430\u0437\u043d\u044b\u0445 \u043e\u0442\u0432\u0435\u0442\u0430.<\/p>\n<h3>\u041d\u0443\u043b\u0435\u0432\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0435 \u0437\u043d\u0430\u0447\u0438\u0442 \u00ab\u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u00bb<\/h3>\n<p>\u0412 \u043c\u043e\u0434\u0435\u043b\u0438 \u0441 \u043f\u043b\u043e\u0449\u0430\u0434\u044c\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043f\u043e\u043f\u0430\u0441\u0442\u044c \u0432 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0443\u044e \u0442\u043e\u0447\u043a\u0443 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e: \u0443 \u0442\u043e\u0447\u043a\u0438 \u043d\u0443\u043b\u0435\u0432\u0430\u044f \u043f\u043b\u043e\u0449\u0430\u0434\u044c. \u041d\u043e \u0432 \u043a\u0430\u043a\u0443\u044e-\u0442\u043e \u0442\u043e\u0447\u043a\u0443 \u0441\u0442\u0440\u0435\u043b\u043e\u043a \u0432\u0441\u0435 \u0440\u0430\u0432\u043d\u043e \u043f\u043e\u043f\u0430\u0434\u0430\u0435\u0442. \u0417\u043d\u0430\u0447\u0438\u0442, P(A) = 0 \u043d\u0435 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u0435 \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u0430 P(A) = 1 &#8212; \u0447\u0442\u043e \u043e\u043d\u043e \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e. \u0412 \u0442\u0430\u043a\u0438\u0445 \u0441\u043b\u0443\u0447\u0430\u044f\u0445 \u0433\u043e\u0432\u043e\u0440\u044f\u0442 \u00ab\u043f\u043e\u0447\u0442\u0438 \u043d\u0430\u0432\u0435\u0440\u043d\u043e\u0435\u00bb. \u0414\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u03a9 \u0441 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044f\u043c\u0438 \u0438\u0441\u0445\u043e\u0434\u043e\u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u043d\u043a\u043e\u0441\u0442\u0438 \u043d\u0435\u0442.<\/p>\n<h3>\u0414\u0440\u0443\u0433\u0430\u044f \u043c\u0435\u0440\u0430: \u0440\u0435\u0430\u043b\u044c\u043d\u044b\u0439 \u0441\u0442\u0440\u0435\u043b\u043e\u043a<\/h3>\n<p>\u0416\u0438\u0432\u043e\u0439 \u0441\u0442\u0440\u0435\u043b\u043e\u043a \u0446\u0435\u043b\u0438\u0442\u0441\u044f \u0432 \u0446\u0435\u043d\u0442\u0440, \u0438 \u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u044f \u0433\u0443\u0449\u0435 \u0443 \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u044b. \u0423\u0434\u043e\u0431\u043d\u0430\u044f \u043c\u043e\u0434\u0435\u043b\u044c &#8212; \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u043e\u0435 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0441 \u0440\u0430\u0437\u0431\u0440\u043e\u0441\u043e\u043c \u03c3 \u043f\u043e \u043a\u0430\u0436\u0434\u043e\u0439 \u043e\u0441\u0438. \u0417\u0434\u0435\u0441\u044c \u03a9 &#8212; \u0432\u0441\u044f \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c (\u043f\u0440\u043e\u043c\u0430\u0445 \u0432\u043e\u0437\u043c\u043e\u0436\u0435\u043d), \u0430 \u043c\u0435\u0440\u0430 \u0437\u0430\u0434\u0430\u043d\u0430 \u043f\u043b\u043e\u0442\u043d\u043e\u0441\u0442\u044c\u044e. \u0414\u043b\u044f \u043a\u0440\u0443\u0433\u0430 \u0440\u0430\u0434\u0438\u0443\u0441\u0430 r \u0432\u043e\u043a\u0440\u0443\u0433 \u0442\u043e\u0447\u043a\u0438 \u043f\u0440\u0438\u0446\u0435\u043b\u0438\u0432\u0430\u043d\u0438\u044f P = 1 &#8212; exp(-r\u00b2 \/ (2\u03c3\u00b2)).<\/p>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\"><span style=\"color: #C678DD\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">math<\/span>\n<span style=\"color: #C678DD\">import<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">random<\/span>\n\n<span style=\"color: #E06C75\">r<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">sigma<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0.3<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #D19A66\">0.3<\/span>   <span style=\"color: #7F848E\"># \u0440\u0430\u0434\u0438\u0443\u0441 \u00ab\u0434\u0435\u0441\u044f\u0442\u043a\u0438\u00bb \u0438 \u0440\u0430\u0437\u0431\u0440\u043e\u0441 \u0441\u0442\u0440\u0435\u043b\u043a\u0430 \u043f\u043e \u043a\u0430\u0436\u0434\u043e\u0439 \u043e\u0441\u0438<\/span>\n<span style=\"color: #E06C75\">N<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">1_000_000<\/span>\n<span style=\"color: #E06C75\">rng<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">random<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">Random<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">42<\/span><span style=\"color: #ABB2BF\">)<\/span>\n\n<span style=\"color: #E06C75\">hits<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #D19A66\">0<\/span>\n<span style=\"color: #C678DD\">for<\/span> <span style=\"color: #E06C75\">_<\/span> <span style=\"color: #56B6C2\">in<\/span> <span style=\"color: #E5C07B\">range<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #E06C75\">N<\/span><span style=\"color: #ABB2BF\">):<\/span>\n    <span style=\"color: #E06C75\">x<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">=<\/span> <span style=\"color: #E06C75\">rng<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">gauss<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">sigma<\/span><span style=\"color: #ABB2BF\">),<\/span> <span style=\"color: #E06C75\">rng<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">gauss<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #D19A66\">0<\/span><span style=\"color: #ABB2BF\">,<\/span> <span style=\"color: #E06C75\">sigma<\/span><span style=\"color: #ABB2BF\">)<\/span>\n    <span style=\"color: #C678DD\">if<\/span> <span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">x<\/span> <span style=\"color: #56B6C2\">+<\/span> <span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">y<\/span> <span style=\"color: #56B6C2\">&lt;=<\/span> <span style=\"color: #E06C75\">r<\/span> <span style=\"color: #56B6C2\">*<\/span> <span style=\"color: #E06C75\">r<\/span><span style=\"color: #ABB2BF\">:<\/span>\n        <span style=\"color: #E06C75\">hits<\/span> <span style=\"color: #56B6C2\">+=<\/span> <span style=\"color: #D19A66\">1<\/span>\n\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"\u0444\u043e\u0440\u043c\u0443\u043b\u0430 1 - exp(-r^2 \/ (2 sigma^2)) = {<\/span><span style=\"color: #D19A66\">1<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">math<\/span><span style=\"color: #56B6C2\">.<\/span><span style=\"color: #E06C75\">exp<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #56B6C2\">-<\/span><span style=\"color: #E06C75\">r<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">*<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">r<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">\/<\/span><span style=\"color: #ABB2BF\"> (<\/span><span style=\"color: #D19A66\">2<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">*<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sigma<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">*<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">sigma<\/span><span style=\"color: #ABB2BF\">))<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span>\n<span style=\"color: #E5C07B\">print<\/span><span style=\"color: #ABB2BF\">(<\/span><span style=\"color: #98C379\">f\"\u0447\u0430\u0441\u0442\u043e\u0442\u0430 \u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u0439 = {<\/span><span style=\"color: #E06C75\">hits<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #56B6C2\">\/<\/span><span style=\"color: #ABB2BF\"> <\/span><span style=\"color: #E06C75\">N<\/span><span style=\"color: #98C379\">:.4f}\"<\/span><span style=\"color: #ABB2BF\">)<\/span><\/code><\/pre>\n<pre style=\"background:#282c34;color:#abb2bf;border-radius:8px;padding:16px 20px;margin:20px 0;overflow-x:auto;font-size:14px;line-height:1.55;font-family:ui-monospace,SFMono-Regular,Menlo,Consolas,monospace\"><code style=\"background:none\">\u0444\u043e\u0440\u043c\u0443\u043b\u0430 1 - exp(-r^2 \/ (2 sigma^2)) = 0.3935\n\u0447\u0430\u0441\u0442\u043e\u0442\u0430 \u043f\u043e\u043f\u0430\u0434\u0430\u043d\u0438\u0439 = 0.3933\n<\/code><\/pre>\n<p>\u0422\u0430 \u0436\u0435 \u00ab\u0434\u0435\u0441\u044f\u0442\u043a\u0430\u00bb, \u043d\u043e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c 0,39 \u0432\u043c\u0435\u0441\u0442\u043e 0,09. \u0421\u043e\u0431\u044b\u0442\u0438\u0435 \u043e\u0434\u043d\u043e, \u043c\u0435\u0440\u044b \u0440\u0430\u0437\u043d\u044b\u0435 &#8212; \u0438 \u043e\u0442\u0432\u0435\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u044b\u0431\u043e\u0440\u043e\u043c \u043c\u0435\u0440\u044b, \u0430 \u043d\u0435 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0435\u0439 \u043c\u0438\u0448\u0435\u043d\u0438. \u041c\u043e\u0434\u0435\u043b\u044c \u0442\u043e\u0436\u0435 \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u043d\u0430\u044f: \u043e\u043d\u0430 \u043d\u0435 \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442 \u0441\u0438\u0441\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441\u0434\u0432\u0438\u0433 \u043f\u0440\u0438\u0446\u0435\u043b\u0430 \u0438 \u0440\u0430\u0437\u043d\u044b\u0439 \u0440\u0430\u0437\u0431\u0440\u043e\u0441 \u043f\u043e \u043e\u0441\u044f\u043c.<\/p>\n<h2 id=\"s5\">\u0412\u044b\u0432\u043e\u0434\u044b<\/h2>\n<ul>\n<li>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430 &#8212; \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0430 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u0445 \u0441\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438 \u0432 [0, 1], \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0449\u0430\u044f \u0442\u0440\u0435\u043c \u0430\u043a\u0441\u0438\u043e\u043c\u0430\u043c \u041a\u043e\u043b\u043c\u043e\u0433\u043e\u0440\u043e\u0432\u0430: \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u044c, P(\u03a9) = 1, \u0441\u0447\u0435\u0442\u043d\u0430\u044f \u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c \u0434\u043b\u044f \u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439.<\/li>\n<li>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e &#8212; \u0442\u0440\u043e\u0439\u043a\u0430 (\u03a9, F, P); \u0441\u0438\u0433\u043c\u0430-\u0430\u043b\u0433\u0435\u0431\u0440\u0430 F \u043d\u0443\u0436\u043d\u0430, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0434\u043b\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u03a9 \u043d\u0435 \u0432\u0441\u0435\u043c \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430\u043c \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u043f\u0438\u0441\u0430\u0442\u044c \u043c\u0435\u0440\u0443.<\/li>\n<li>\u041c\u0435\u0440\u0430 \u041b\u0435\u0431\u0435\u0433\u0430 &#8212; \u043d\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c; \u043d\u043e\u0440\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u0430\u044f \u043f\u043b\u043e\u0449\u0430\u0434\u044c P(A) = \u03bb(A) \/ \u03bb(\u03a9) \u0434\u0430\u0435\u0442 \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c (r \/ R)\u00b2 \u0434\u043b\u044f \u00ab\u0434\u0435\u0441\u044f\u0442\u043a\u0438\u00bb.<\/li>\n<li>\u00ab\u041d\u0430\u0443\u0434\u0430\u0447\u0443\u00bb \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u044f\u0432\u043d\u043e\u0433\u043e \u0432\u044b\u0431\u043e\u0440\u0430 \u043c\u0435\u0440\u044b: \u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u044b\u0439 \u0440\u0430\u0434\u0438\u0443\u0441 \u0438 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0440\u0430\u0437\u0431\u0440\u043e\u0441 \u0434\u0430\u044e\u0442 0,30 \u0438 0,39 \u0432\u043c\u0435\u0441\u0442\u043e 0,09.<\/li>\n<li>\u041d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u043e\u0441\u0442\u044c \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c &#8212; \u0440\u0430\u0437\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430; \u043d\u0443\u043b\u0435\u0432\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0435 \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442 \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c.<\/li>\n<\/ul>\n<h2 id=\"s6\">\u0413\u0434\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \/ \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0439<\/h2>\n<p>\u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e &#8212; \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442 \u0434\u043b\u044f \u0432\u0441\u0435\u0433\u043e, \u0447\u0442\u043e \u0432 IT \u0440\u0430\u0431\u043e\u0442\u0430\u0435\u0442 \u0441\u043e \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u043e\u0441\u0442\u044c\u044e: A\/B-\u0442\u0435\u0441\u0442\u043e\u0432, \u043e\u0446\u0435\u043d\u043a\u0438 \u0440\u0438\u0441\u043a\u043e\u0432, \u043c\u0435\u0442\u043e\u0434\u0430 \u041c\u043e\u043d\u0442\u0435-\u041a\u0430\u0440\u043b\u043e, \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u0438\u0432\u043d\u044b\u0445 \u043c\u043e\u0434\u0435\u043b\u0435\u0439 \u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u043f\u043e\u0442\u0435\u0440\u044c \u0432 \u043c\u0430\u0448\u0438\u043d\u043d\u043e\u043c \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0438. \u041f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u0435, \u043a\u0430\u043a\u0430\u044f \u043c\u0435\u0440\u0430 \u0441\u0442\u043e\u0438\u0442 \u0437\u0430 \u00ab\u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u043c\u00bb \u0432\u044b\u0431\u043e\u0440\u043e\u043c, \u0441\u043f\u0430\u0441\u0430\u0435\u0442 \u043e\u0442 \u043e\u0448\u0438\u0431\u043e\u043a \u0432\u0440\u043e\u0434\u0435 \u00ab\u0440\u0430\u0432\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u0440\u0430\u0434\u0438\u0443\u0441\u0430\u00bb \u0432 \u0441\u0438\u043c\u0443\u043b\u044f\u0446\u0438\u044f\u0445 \u0438 \u0432\u044b\u0431\u043e\u0440\u043a\u0430\u0445.<\/p>\n<div class=\"oj-cta\" style=\"background:#fbf4e4;border-left:4px solid #c9962b;border-radius:8px;padding:16px 20px;margin:24px 0\">\n<p style=\"margin:0 0 8px\"><strong>\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0442\u0435\u043c\u0443 \u043d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435<\/strong><\/p>\n<p>\u0415\u0441\u043b\u0438 \u0445\u043e\u0447\u0435\u0442\u0441\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u043d\u043e \u043f\u043e\u0434\u0442\u044f\u043d\u0443\u0442\u044c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430, \u0430\u043d\u0430\u043b\u0438\u0437, \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0430\u043b\u0433\u0435\u0431\u0440\u0443 \u0438 \u0442\u0435\u043e\u0440\u0438\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439 \u043f\u043e\u0434 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438, \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u043a\u0443\u0440\u0441 <a href=\"https:\/\/otus.ru\/lessons\/prikladnaya-matematika\/?utm_source=oj&amp;utm_medium=article&amp;utm_campaign=mera-i-veroyatnost&amp;utm_content=course\">\u00ab\u0411\u0430\u0437\u043e\u0432\u0430\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0434\u043b\u044f \u0446\u0438\u0444\u0440\u043e\u0432\u044b\u0445 \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u0439\u00bb<\/a>. \u0420\u0430\u0437\u043e\u0431\u0440\u0430\u0442\u044c \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0442\u0435\u043c\u044b \u0441 \u043f\u0440\u0435\u043f\u043e\u0434\u0430\u0432\u0430\u0442\u0435\u043b\u044f\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u043d\u0430 <a href=\"https:\/\/otus.ru\/events\/?utm_source=oj&amp;utm_medium=article&amp;utm_campaign=mera-i-veroyatnost&amp;utm_content=events\">\u0431\u0435\u0441\u043f\u043b\u0430\u0442\u043d\u044b\u0445 \u043e\u0442\u043a\u0440\u044b\u0442\u044b\u0445 \u0443\u0440\u043e\u043a\u0430\u0445 Otus<\/a>.<\/p>\n<\/div>\n<h2 id=\"s7\">FAQ<\/h2>\n<p><strong>\u0427\u0435\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u043d\u0430\u044f \u043c\u0435\u0440\u0430 \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f?<\/strong><br \/>\n\u041c\u0435\u0440\u0430 P \u0437\u0430\u0434\u0430\u043d\u0430 \u043d\u0430 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u0445 (\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430\u0445), \u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f F(x) = P(X \u2264 x) &#8212; \u043d\u0430 \u0447\u0438\u0441\u043b\u0430\u0445 \u0438 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442 \u043e\u0434\u043d\u0443 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0443\u044e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443. \u0414\u043b\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d \u043d\u0430 \u043f\u0440\u044f\u043c\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043e\u0434\u043d\u043e\u0437\u043d\u0430\u0447\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0443\u044e \u043c\u0435\u0440\u0443.<\/p>\n<p><strong>\u041c\u043e\u0436\u043d\u043e \u043b\u0438 \u043e\u0431\u043e\u0439\u0442\u0438\u0441\u044c \u0431\u0435\u0437 \u0441\u0438\u0433\u043c\u0430-\u0430\u043b\u0433\u0435\u0431\u0440\u044b, \u0435\u0441\u043b\u0438 \u03a9 \u043a\u043e\u043d\u0435\u0447\u043d\u043e?<\/strong><br \/>\n\u0414\u0430: \u0434\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0438\u043b\u0438 \u0441\u0447\u0435\u0442\u043d\u043e\u0433\u043e \u03a9 \u043c\u043e\u0436\u043d\u043e \u0432\u0437\u044f\u0442\u044c \u0432\u0441\u0435 \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430, \u0438 \u043d\u0438\u043a\u0430\u043a\u0438\u0445 \u043f\u0440\u043e\u0431\u043b\u0435\u043c \u0441 \u0438\u0437\u043c\u0435\u0440\u0438\u043c\u043e\u0441\u0442\u044c\u044e \u043d\u0435 \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442. \u0421\u0438\u0433\u043c\u0430-\u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u043e\u0439 \u0434\u043b\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u044b\u0445 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432.<\/p>\n<p><strong>\u0427\u0435\u043c \u0441\u0447\u0435\u0442\u043d\u0430\u044f \u0430\u0434\u0434\u0438\u0442\u0438\u0432\u043d\u043e\u0441\u0442\u044c \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0439?<\/strong><br \/>\n\u041a\u043e\u043d\u0435\u0447\u043d\u0430\u044f \u0442\u0440\u0435\u0431\u0443\u0435\u0442 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u043b\u044f \u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439, \u0441\u0447\u0435\u0442\u043d\u0430\u044f &#8212; \u0434\u043b\u044f \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u043e\u0439 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0441\u0442\u0438. \u0421\u0447\u0435\u0442\u043d\u0430\u044f \u0441\u0438\u043b\u044c\u043d\u0435\u0435 \u0438 \u043d\u0443\u0436\u043d\u0430 \u0434\u043b\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, 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\u0441\u043e\u0431\u044b\u0442\u0438\u0439 F \u0441\u0442\u0430\u0432\u0438\u0442 \u0432 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0438\u0435 \u0447\u0438\u0441\u043b\u043e P(A) \u043e\u0442 0 \u0434\u043e 1 \u0442\u0430\u043a, \u0447\u0442\u043e P(\u03a9) = 1 \u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u0438\u044f \u043f\u043e\u043f\u0430\u0440\u043d\u043e \u043d\u0435\u0441\u043e\u0432\u043c\u0435\u0441\u0442\u043d\u044b\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0440\u0430\u0432\u043d\u0430 \u0441\u0443\u043c\u043c\u0435 \u0438\u0445 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439. \u0418\u043d\u0430\u0447\u0435 \u0433\u043e\u0432\u043e\u0440\u044f, \u044d\u0442\u043e \u043c\u0435\u0440\u0430 \u0441 \u043f\u043e\u043b\u043d\u043e\u0439 \u043c\u0430\u0441\u0441\u043e\u0439 1. \u0412\u043c\u0435\u0441\u0442\u0435 \u0441 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