{"id":34102,"date":"2021-03-29T13:00:21","date_gmt":"2021-03-29T13:00:21","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34102"},"modified":"2025-08-16T07:05:38","modified_gmt":"2025-08-16T07:05:38","slug":"%e7%a2%ba%e7%8e%87%e8%a8%88%e7%ae%97%e3%81%ae%e3%81%9f%e3%82%81%e3%81%ae%e6%9c%89%e7%94%a8%e3%81%aa%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e7%a2%ba%e7%8e%87%e8%a8%88%e7%ae%97%e3%81%ae%e3%81%9f%e3%82%81%e3%81%ae%e6%9c%89%e7%94%a8%e3%81%aa%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u78ba\u7387\u8a08\u7b97\u306e\u305f\u3081\u306e\u6709\u7528\u306a\u5b9a\u7406"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u78ba\u7387\u8a08\u7b97\u306e\u305f\u3081\u306e\u6709\u7528\u306a\u5b9a\u7406<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u8981\u7d04<\/strong><br \/><em>\u3053\u306e\u6388\u696d\u3067\u306f\u3001\u78ba\u7387\u8a08\u7b97\u306b\u6709\u7528\u306a\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u3044\u304f\u3064\u304b\u306e\u89e3\u6cd5\u4ed8\u304d\u6f14\u7fd2\u3092\u63d0\u793a\u3057\u3001\u8a3c\u660e\u3084\u63a8\u8ad6\u3092\u542b\u307f\u307e\u3059\u3002\u6f14\u7fd2\u306f\u88dc\u96c6\u5408\u306e\u78ba\u7387\u3001\u96c6\u5408\u306e\u5305\u542b\u3001\u4e8b\u8c61\u306e\u53ce\u675f\u3068\u3044\u3063\u305f\u30c6\u30fc\u30de\u3092\u6271\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6f14\u7fd2\u3092\u4fee\u4e86\u3059\u308b\u3053\u3068\u3067\u3001\u78ba\u7387\u8ad6\u306e\u5b66\u7fd2\u3092\u6df1\u3081\u308b\u305f\u3081\u306e\u5805\u56fa\u306a\u57fa\u790e\u3092\u8eab\u306b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u7fd2\u76ee\u6a19:<\/strong><br \/>\n\u3053\u306e\u6388\u696d\u3092\u4fee\u4e86\u3057\u305f\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059:\n<\/p>\n<ol>\n<li><strong>\u78ba\u7387\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u3092\u8a3c\u660e\u3059\u308b<\/strong><\/li>\n<\/ol>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/SSkPFP5FpKM\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify;\">\u4ee5\u4e0b\u3067\u306f\u3001\u78ba\u7387\u8ad6\u306b\u304a\u3051\u308b\u3044\u304f\u3064\u304b\u306e\u6709\u7528\u306a\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u305f\u6f14\u7fd2\uff08\u89e3\u7b54\u4ed8\u304d\uff09\u306e\u30ac\u30a4\u30c9\u3092\u793a\u3057\u307e\u3059\u3002\u81ea\u5206\u3067\u89e3\u3044\u3066\u304b\u3089\u7d50\u679c\u3092\u6bd4\u8f03\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044 &gt;:D<\/p>\n<ol style=\"text-align: justify;\">\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=111s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A^c) = 1 -P(A)<\/span> \u3092\u8a3c\u660e\u3057\u3001<\/span><\/a> \u3053\u308c\u306b\u57fa\u3065\u3044\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">P(\\emptyset) = 0<\/span> \u3092\u8ad6\u3058\u308b\u63a8\u8ad6\u3092\u884c\u3044\u306a\u3055\u3044<\/strong><br \/>\n<span class=\"collapseomatic \" id=\"id6aa1c574a8edd\"  tabindex=\"0\" title=\"\u89e3\u7b54\u3092\u8868\u793a\"    >\u89e3\u7b54\u3092\u8868\u793a<\/span><div id=\"target-id6aa1c574a8edd\" class=\"collapseomatic_content \">\n<p style=\"text-align: justify;\">\u78ba\u7387\u6e2c\u5ea6\u306e<a href=\"https:\/\/toposuranos.com\/el-espacio-de-probabilidades-medida-de-probabilidad\/\" target=\"_blank\" rel=\"noopener\">\u5b9a\u7fa9<\/a>\u3088\u308a\u3001<span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u304c\u4efb\u610f\u306e\u53ef\u6e2c\u4e8b\u8c61\u3067\u3042\u308b\u3068\u304d\u3001\u6b21\u304c\u6210\u308a\u7acb\u3061\u307e\u3059<\/p>\n<table>\n<tbody>\n<tr>\n<td>[a]<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">0\\leq P(A) \\leq 1<\/span><\/td>\n<\/tr>\n<tr>\n<td>[b]<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\cap B = \\emptyset \\rightarrow P(A\\cup B) = P(A) + P(B)<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(\\Omega) = 1<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u3055\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">A\\cap A^c = \\emptyset<\/span> \u3067\u3042\u308b\u306e\u3067\u3001[b] \u3088\u308a\u6b21\u304c\u6210\u308a\u7acb\u3061\u307e\u3059:<\/p>\n<table>\n<tbody>\n<tr>\n<td>[d]<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\cap A^c = \\emptyset \\rightarrow P(A\\cup A^c) = P(A) + P(A^c)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">A\\cap A^c = \\emptyset<\/span> \u306f\u5e38\u306b\u771f\u3067\u3042\u308a\u3001\u304b\u3064 <span class=\"katex-eq\" data-katex-display=\"false\">A\\cup A^c = \\Omega<\/span> \u3067\u3042\u308b\u306e\u3067\u3001\u6b21\u304c\u6210\u308a\u7acb\u3061\u307e\u3059<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">1=P(\\Omega) = P(A\\cup A^c) = P(A) + P(A^c)<\/span>\n<p style=\"text-align: justify;\">\u3057\u305f\u304c\u3063\u3066<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A^c) = 1-P(A)<\/span>\n<p style=\"text-align: justify;\">\u3053\u308c\u304c\u793a\u3057\u305f\u304b\u3063\u305f\u3053\u3068\u3067\u3059\u3002<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(\\emptyset)=0<\/span> \u3092\u793a\u3059\u306b\u306f\u3001\u5148\u307b\u3069\u8a3c\u660e\u3057\u305f\u95a2\u4fc2\u306b\u304a\u3044\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">A=\\Omega<\/span> \u3092\u3068\u308c\u3070\u5341\u5206\u3067\u3042\u308a\u3001\u6b21\u304c\u5f97\u3089\u308c\u307e\u3059<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(\\emptyset) = P(\\Omega^c) =1 - P(\\Omega) = 1-1 = 0<\/span>\n<\/div><\/li>\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=534s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">a) <span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B \\rightarrow P(B\\setminus A) = P(B) - P(A)<\/span> \u3092\u8a3c\u660e\u305b\u3088<\/span><\/a>\u3002\u3053\u306e\u7b49\u5f0f\u306f\u4e00\u822c\u306b\u6210\u308a\u7acb\u3064\u304b\uff1f<\/strong><strong>b) <span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B \\rightarrow P(B)\\leq P(A)<\/span> \u3092\u8a3c\u660e\u305b\u3088<\/strong><span class=\"collapseomatic \" id=\"id6aa1c574a91b3\"  tabindex=\"0\" title=\"\u89e3\u7b54\u3092\u8868\u793a a)\"    >\u89e3\u7b54\u3092\u8868\u793a a)<\/span><div id=\"target-id6aa1c574a91b3\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td>(1)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B<\/span>; \u524d\u63d0<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv A\\cap B = A<\/span><\/td>\n<\/tr>\n<tr>\n<td>(2)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">B\\setminus A = B\\cap A^c<\/span>; \u96c6\u5408\u8ad6\u306e\u5b9a\u7fa9<\/td>\n<\/tr>\n<tr>\n<td>(3)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">B= (B\\cap A) \\cup (B\\cap A^c)<\/span>; \u96c6\u5408\u306e\u6027\u8cea<\/td>\n<\/tr>\n<tr>\n<td>(4)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(B\\cap A)\\cap (B\\cap A^c)=\\emptyset<\/span>; \u96c6\u5408\u306e\u6027\u8cea<\/td>\n<\/tr>\n<tr>\n<td>(5)<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B)= P[(B\\cap A) \\cup (B\\cap A^c)]<\/span>; (3)\u3088\u308a<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B)= P (B\\cap A) + P(B\\cap A^c)<\/span>; (4) \u3068\u78ba\u7387\u6e2c\u5ea6\u306e\u5b9a\u7fa9\u3088\u308a<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B)= P (B\\cap A) + P(B\\setminus A)<\/span>; (2)\u3088\u308a<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> P(B\\setminus A) =P(B) - P (B\\cap A) <\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{P(B\\setminus A) =P(B) - P (A) }<\/span>; (1)\u3088\u308a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\">\u3057\u305f\u304c\u3063\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">{\\{A\\subseteq B\\}\\vdash P(B\\setminus A) = P(B) - P(A)}.<\/span>\n<p style=\"text-align: justify;\">\u3053\u306e\u7b49\u5f0f\u306f\u4e00\u822c\u306b\u306f\u6210\u308a\u7acb\u305f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u306f <span class=\"katex-eq\" data-katex-display=\"false\">A\\subseteq B<\/span> \u304c\u6210\u7acb\u3059\u308b\u5834\u5408\u306b\u306e\u307f\u5f97\u3089\u308c\u308b\u3082\u306e\u3067\u3059\u3002\u3053\u306e\u8b70\u8ad6\u304b\u3089\u3001\u3082\u3057\u305d\u308c\u304c\u6e80\u305f\u3055\u308c\u306a\u3044\u5834\u5408\u306b\u306f <span class=\"katex-eq\" data-katex-display=\"false\">P(B\\setminus A) = P(B) - P(A\\cap B).<\/span> \u3068\u306a\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<span class=\"collapseomatic \" id=\"id6aa1c574a93f6\"  tabindex=\"0\" title=\"\u89e3\u7b54\u3092\u8868\u793a b)\"    >\u89e3\u7b54\u3092\u8868\u793a b)<\/span><div id=\"target-id6aa1c574a93f6\" class=\"collapseomatic_content \">\n<p style=\"text-align: justify;\">a) \u3067\u306e\u8b70\u8ad6\u306b\u57fa\u3065\u3051\u3070\u6b21\u304c\u5f97\u3089\u308c\u307e\u3059:<\/p>\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\{A\\subseteq B\\}\\vdash P(B\\setminus A) = P(B) - P(A)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv \\{A\\subseteq B\\}\\vdash P(A) + P(B\\setminus A) = P(B)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u6700\u5f8c\u306b\u3001<span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> \u306f\u78ba\u7387\u6e2c\u5ea6\u3067\u3042\u308b\u305f\u3081\u3001<span class=\"katex-eq\" data-katex-display=\"false\">\\forall X (P(X)\\geq 0),<\/span> \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u6b21\u304c\u5c0e\u304b\u308c\u307e\u3059:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">{\\{A\\subseteq B\\}\\vdash P(A) \\leq P(B)}.<\/span>\n<\/div>\n<p>&nbsp;<\/li>\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=892s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">a) <span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A) + P(B) - P(A\\cup B).<\/span> \u3092\u8a3c\u660e\u305b\u3088<\/span><\/a>\u3002\u8a3c\u660e\u306b\u306f\u56f3\u3092\u6dfb\u3048\u306a\u3055\u3044\u3002<\/strong><strong>b) \u4e0a\u306e\u7d50\u679c\u3092\u7528\u3044\u3066 <span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) \\leq P(A) + P(B)<\/span> \u3092\u8a3c\u660e\u305b\u3088<\/strong><span class=\"collapseomatic \" id=\"id6aa1c574a950e\"  tabindex=\"0\" title=\"\u89e3\u7b54\u3092\u8868\u793a a)\"    >\u89e3\u7b54\u3092\u8868\u793a a)<\/span><div id=\"target-id6aa1c574a950e\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\cup B = (A\\triangle B) \\cup (A\\cap B)<\/span>; \u96c6\u5408\u306e\u6027\u8cea<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">A\\triangle B := (A\\setminus B) \\cup (B\\setminus A)<\/span>; \u5bfe\u79f0\u5dee\u306e\u5b9a\u7fa9<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(A\\triangle B)\\cap ( A \\cap B) = \\emptyset<\/span>; \u96c6\u5408\u306e\u6027\u8cea<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(A\\setminus B)\\cap (B\\setminus A) = \\emptyset<\/span>; \u96c6\u5408\u306e\u6027\u8cea<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P[(A\\triangle B) \\cup (A\\cap B)]<\/span>; (1)\u3088\u308a<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A\\triangle B) + P(A\\cap B)]<\/span>; (3)\u3088\u308a<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A\\setminus B) + P(B\\setminus A) + P(A\\cap B)]<\/span>; (2,4)\u3088\u308a<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(B\\setminus A) = P(B) - P(A\\cap B)<\/span>; \u6f14\u7fd22\u306e\u7d50\u679c\u3092\u9069\u7528<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(7)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\setminus B) = P(A) - P(A\\cap B)<\/span>; (6) \u3068\u540c\u69d8<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(8)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cup B) = P(A) - P(A\\cap B) + P(B) - P(A\\cap B) + P(A\\cap B)<\/span>; (5,6,7)\u3088\u308a<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{P(A\\cup B) = P(A) + P(B) - P(A\\cap B)}. <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<span class=\"collapseomatic \" id=\"id6aa1c574a969c\"  tabindex=\"0\" title=\"\u89e3\u7b54\u3092\u8868\u793a PART b)\"    >\u89e3\u7b54\u3092\u8868\u793a PART b)<\/span><div id=\"target-id6aa1c574a969c\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash P(A\\cup B) = P(A) + P(B) - P(A\\cap B)<\/span>; a) \u306e\u7d50\u679c<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv\\; \\vdash P(A\\cup B) + P(A\\cap B) = P(A) + P(B) <\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv\\; \\vdash {P(A\\cup B) \\leq P(A) + P(B)} <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/li>\n<li><strong><a href=\"https:\/\/www.youtube.com\/watch?v=SSkPFP5FpKM&amp;t=1625s\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #ff0000;\">\u3082\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">\\{E_n\\}<\/span> \u304c\u7121\u9650\u306e\u4e8b\u8c61\u65cf\u3067\u3042\u308b\u306a\u3089<\/span> <\/a>\u6b21\u306e\u3088\u3046\u306b <span class=\"katex-eq\" data-katex-display=\"false\">E_1\\supseteq E_2 \\supseteq E_2 \\supseteq \\cdots \\supseteq E_n \\supseteq E_{n+1}\\supseteq \\cdots.<\/span> \u304c\u6210\u308a\u7acb\u3064\u3002\u3053\u308c\u3092\u8a3c\u660e\u305b\u3088:<\/strong>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = \\lim_{n\\to \\infty}P(E_n)<\/span>\n<span class=\"collapseomatic \" id=\"id6aa1c574a97a1\"  tabindex=\"0\" title=\"\u89e3\u7b54\u3092\u8868\u793a\"    >\u89e3\u7b54\u3092\u8868\u793a<\/span><div id=\"target-id6aa1c574a97a1\" class=\"collapseomatic_content \">\n<table>\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">E_n \\supseteq E_{n+1}<\/span>; \u4eee\u5b9a<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">E_n^c \\subseteq E_{n+1}^c<\/span>; (1) \u3088\u308a\u88dc\u96c6\u5408\u3067<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle(E_n^c \\subseteq E_{n+1}^c) \\rightarrow P\\left( \\bigcup_{n=1}^\\infty E_n^c \\right)= \\lim_{n\\to\\infty}P(E_n^c)<\/span>; \u9023\u7d9a\u6027\u306e\u6027\u8cea<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigcup_{n=1}^\\infty E_n^c = \\left( \\bigcap_{n=1}^\\infty E_n \\right)^c<\/span>; \u30c9\u30fb\u30e2\u30eb\u30ac\u30f3\u306e\u6cd5\u5247<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P\\left(E_n^c\\right) = 1 - P(E_n)<\/span>; \u6f14\u7fd21\u3067\u8a3c\u660e\u6e08\u307f<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P\\left(\\left[ \\bigcap_{n=1}^\\infty E_n\\right]^c \\right) = \\lim_{n\\to\\infty}[1-P(E_n)] = 1 - \\lim_{n\\to\\infty}P(E_n)<\/span>; (2,4,5) \u3092 (3) \u306b\u9069\u7528<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 1 - P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = 1 - \\lim_{n\\to\\infty}P(E_n) <\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">{\\displaystyle P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = \\lim_{n\\to\\infty}P(E_n)} <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\therefore\\{E_n \\supseteq E_{n+1}\\}\\vdash P\\left( \\bigcap_{n=1}^\\infty E_n \\right) = \\lim_{n\\to\\infty}P(E_n).<\/span>\n<p>&nbsp;<\/li>\n<\/ol>\n<\/div>\n<p style=\"text-align: justify;\">\u3053\u308c\u3089\u306e\u6f14\u7fd2\u3092\u89e3\u304f\u3053\u3068\u3067\u3001\u78ba\u7387\u8ad6\u306e\u5b66\u7fd2\u3092\u7d9a\u3051\u308b\u305f\u3081\u306e\u652f\u3048\u3068\u306a\u308b\u6700\u521d\u306e\u67f1\u3092\u7bc9\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u78ba\u7387\u8a08\u7b97\u306e\u305f\u3081\u306e\u6709\u7528\u306a\u5b9a\u7406 \u8981\u7d04\u3053\u306e\u6388\u696d\u3067\u306f\u3001\u78ba\u7387\u8a08\u7b97\u306b\u6709\u7528\u306a\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u3044\u304f\u3064\u304b\u306e\u89e3\u6cd5\u4ed8\u304d\u6f14\u7fd2\u3092\u63d0\u793a\u3057\u3001\u8a3c\u660e\u3084\u63a8\u8ad6\u3092\u542b\u307f\u307e\u3059\u3002\u6f14\u7fd2\u306f\u88dc\u96c6\u5408\u306e\u78ba\u7387\u3001\u96c6\u5408\u306e\u5305\u542b\u3001\u4e8b\u8c61\u306e\u53ce\u675f\u3068\u3044\u3063\u305f\u30c6\u30fc\u30de\u3092\u6271\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6f14\u7fd2\u3092\u4fee\u4e86\u3059\u308b\u3053\u3068\u3067\u3001\u78ba\u7387\u8ad6\u306e\u5b66\u7fd2\u3092\u6df1\u3081\u308b\u305f\u3081\u306e\u5805\u56fa\u306a\u57fa\u790e\u3092\u8eab\u306b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19: \u3053\u306e\u6388\u696d\u3092\u4fee\u4e86\u3057\u305f\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059: \u78ba\u7387\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u3092\u8a3c\u660e\u3059\u308b \u4ee5\u4e0b\u3067\u306f\u3001\u78ba\u7387\u8ad6\u306b\u304a\u3051\u308b\u3044\u304f\u3064\u304b\u306e\u6709\u7528\u306a\u5b9a\u7406\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u305f\u6f14\u7fd2\uff08\u89e3\u7b54\u4ed8\u304d\uff09\u306e\u30ac\u30a4\u30c9\u3092\u793a\u3057\u307e\u3059\u3002\u81ea\u5206\u3067\u89e3\u3044\u3066\u304b\u3089\u7d50\u679c\u3092\u6bd4\u8f03\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044 &gt;:D \u3092\u8a3c\u660e\u3057\u3001 \u3053\u308c\u306b\u57fa\u3065\u3044\u3066 \u3092\u8ad6\u3058\u308b\u63a8\u8ad6\u3092\u884c\u3044\u306a\u3055\u3044 a) \u3092\u8a3c\u660e\u305b\u3088\u3002\u3053\u306e\u7b49\u5f0f\u306f\u4e00\u822c\u306b\u6210\u308a\u7acb\u3064\u304b\uff1fb) \u3092\u8a3c\u660e\u305b\u3088 &nbsp; a) \u3092\u8a3c\u660e\u305b\u3088\u3002\u8a3c\u660e\u306b\u306f\u56f3\u3092\u6dfb\u3048\u306a\u3055\u3044\u3002b) \u4e0a\u306e\u7d50\u679c\u3092\u7528\u3044\u3066 \u3092\u8a3c\u660e\u305b\u3088 &nbsp; \u3082\u3057 \u304c\u7121\u9650\u306e\u4e8b\u8c61\u65cf\u3067\u3042\u308b\u306a\u3089 \u6b21\u306e\u3088\u3046\u306b \u304c\u6210\u308a\u7acb\u3064\u3002\u3053\u308c\u3092\u8a3c\u660e\u305b\u3088: \u3053\u308c\u3089\u306e\u6f14\u7fd2\u3092\u89e3\u304f\u3053\u3068\u3067\u3001\u78ba\u7387\u8ad6\u306e\u5b66\u7fd2\u3092\u7d9a\u3051\u308b\u305f\u3081\u306e\u652f\u3048\u3068\u306a\u308b\u6700\u521d\u306e\u67f1\u3092\u7bc9\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n","protected":false},"author":1,"featured_media":26394,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":8,"footnotes":""},"categories":[1300,1368],"tags":[],"class_list":["post-34102","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category--ja","category-1368"],"yoast_head":"<!-- This site is optimized with the Yoast 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