{"id":392,"date":"2023-08-01T04:39:10","date_gmt":"2023-08-01T04:39:10","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e7%a2%ba%e7%8e%87%e3%81%ae%e5%85%ac%e5%bc%8f\/"},"modified":"2023-08-01T04:39:10","modified_gmt":"2023-08-01T04:39:10","slug":"%e7%a2%ba%e7%8e%87%e3%81%ae%e5%85%ac%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e7%a2%ba%e7%8e%87%e3%81%ae%e5%85%ac%e5%bc%8f\/","title":{"rendered":"\u78ba\u7387\u306e\u516c\u5f0f"},"content":{"rendered":"

\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u78ba\u7387\u516c\u5f0f\u3068\u306f\u4f55\u304b\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u78ba\u7387\u8ad6\u306e\u3059\u3079\u3066\u306e\u516c\u5f0f\u3068\u3001\u305d\u306e\u5fdc\u7528\u4f8b\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>\n

<\/span>\u30e9\u30d7\u30e9\u30b9\u306e\u6cd5\u5247\u306e\u516c\u5f0f<\/span><\/h2>\n

\u30e9\u30d7\u30e9\u30b9\u306e\u6cd5\u5247\u3068\u3082\u547c\u3070\u308c\u308b\u30e9\u30d7\u30e9\u30b9\u306e\u6cd5\u5247\u306f\u3001\u4e8b\u8c61\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u6cd5\u5247\u3067\u3059\u3002<\/p>\n

\u30e9\u30d7\u30e9\u30b9\u306e\u6cd5\u5247\u306b\u3088\u308c\u3070\u3001\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u306f\u3001\u6709\u5229\u306a\u30b1\u30fc\u30b9\u306e\u6570\u3092\u53ef\u80fd\u306a\u30b1\u30fc\u30b9\u306e\u7dcf\u6570\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u7b49\u3057\u3044\u3068\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u305d\u306e\u30a4\u30d9\u30f3\u30c8\u3092\u6e80\u305f\u3059\u30b1\u30fc\u30b9\u3092\u53ef\u80fd\u306a\u7d50\u679c\u306e\u6570\u3067\u5272\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n

\u3057\u305f\u304c\u3063\u3066\u3001\u30e9\u30d7\u30e9\u30b9\u306e\u6cd5\u5247\u306e\u5f0f\u306f<\/strong>\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n

\"P(A)=\\cfrac{\\text{casos<\/p>\n<\/p>\n

\u27a4<\/span>\u53c2\u7167:<\/strong>\u30e9\u30d7\u30e9\u30b9\u5247\u306e\u4f8b<\/a><\/div>\n

<\/span>\u9006\u30a4\u30d9\u30f3\u30c8\u306e\u516c\u5f0f<\/span><\/h2>\n

\u3042\u308b\u4e8b\u8c61\u306e\u78ba\u7387\u306f\u30011 \u304b\u3089\u305d\u306e\u53cd\u5bfe\u306e\u4e8b\u8c61\u306e\u78ba\u7387\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u3042\u308b\u4e8b\u8c61\u306e\u78ba\u7387\u3068\u305d\u306e\u53cd\u5bfe\u306e\u4e8b\u8c61\u306e\u78ba\u7387\u306e\u5408\u8a08\u306f 1 \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n

\"P\\bigl(A\\bigr)=1-P\\bigl(\\overline{A}\\bigr)\"<\/p>\n<\/p>\n

\u305f\u3068\u3048\u3070\u3001\u6b21\u306e\u78ba\u7387\u7279\u6027\u3092\u4f7f\u7528\u3057\u3066\u4ed6\u306e\u6570\u5b57\u304c\u51fa\u308b\u78ba\u7387\u3092\u6c7a\u5b9a\u3067\u304d\u308b\u305f\u3081\u3001\u6570\u5b57 5 \u304c\u51fa\u308b\u78ba\u7387\u306f 0.167 \u3067\u3059\u3002 <\/p>\n<\/p>\n

\"P(5)=0,167\"<\/p>\n<\/p>\n

\"P(1,<\/p>\n<\/p>\n

<\/span>\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306e\u5f0f<\/span><\/h2>\n

\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306f\u3001\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3068\u3082\u547c\u3070\u308c\u3001\u5225\u306e\u30a4\u30d9\u30f3\u30c8 B \u304c\u767a\u751f\u3057\u305f\u5834\u5408\u306b\u30a4\u30d9\u30f3\u30c8 A \u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u3092\u793a\u3059\u7d71\u8a08\u7684\u5c3a\u5ea6\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6761\u4ef6\u4ed8\u304d\u78ba\u7387 P(A|B) \u306f\u3001\u30a4\u30d9\u30f3\u30c8 B \u304c\u3059\u3067\u306b\u767a\u751f\u3057\u305f\u5f8c\u306b\u30a4\u30d9\u30f3\u30c8 A \u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n

\u30a4\u30d9\u30f3\u30c8 B \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u306e\u30a4\u30d9\u30f3\u30c8 A \u306e\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306f\u3001\u30a4\u30d9\u30f3\u30c8 A \u3068\u30a4\u30d9\u30f3\u30c8 B \u306e\u4ea4\u5dee\u306e\u78ba\u7387\u3092\u30a4\u30d9\u30f3\u30c8 B \u306e\u78ba\u7387\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306e\u5f0f\u306f<\/strong>\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>\n<\/p>\n

\"P(A|B)=\\cfrac{P(A\\cap<\/p>\n<\/p>\n

\u27a4<\/span>\u53c2\u7167:<\/strong>\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306e\u4f8b<\/a><\/div>\n

<\/span>\u30a4\u30d9\u30f3\u30c8\u306e\u548c\u96c6\u5408\u306e\u516c\u5f0f<\/span><\/h2>\n

2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8 A \u3068 B \u306e\u548c\u96c6\u5408\u306f\u3001A\u3001B\u3001\u307e\u305f\u306f\u4e21\u65b9\u306b\u5b58\u5728\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u306e\u30bb\u30c3\u30c8\u3067\u3059\u3002 2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u7d50\u5408\u306f\u8a18\u53f7 \u22c3 \u3067\u8868\u73fe\u3055\u308c\u308b\u305f\u3081\u3001\u30a4\u30d9\u30f3\u30c8 A \u3068 B \u306e\u7d50\u5408\u306f A\u22c3B \u3068\u66f8\u304b\u308c\u307e\u3059\u3002<\/p>\n

2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u7d50\u5408\u3059\u308b\u78ba\u7387\u306f\u3001\u6700\u521d\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387\u306b 2 \u756a\u76ee\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387\u3092\u52a0\u3048\u3001\u30a4\u30d9\u30f3\u30c8\u306e\u4ea4\u5dee\u306e\u78ba\u7387\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u3064\u307e\u308a\u3001 2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u7d50\u5408\u3059\u308b\u78ba\u7387\u306e\u516c\u5f0f\u306f\u3001<\/strong> P(A\u22c3B)=P(A)+P(B)-P(A\u22c2B) \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n

\"P(A\\cup<\/p>\n<\/p>\n

\u305f\u3060\u3057\u30012 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u306b\u4e92\u63db\u6027\u304c\u306a\u3044\u5834\u5408\u30012 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u9593\u306e\u4ea4\u5dee\u306f\u30bc\u30ed\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u4e92\u63db\u6027\u306e\u306a\u3044\u30a4\u30d9\u30f3\u30c8\u304c\u7d50\u5408\u3059\u308b\u78ba\u7387\u306f\u3001\u5404\u30a4\u30d9\u30f3\u30c8\u306e\u767a\u751f\u78ba\u7387\u3092\u52a0\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002 <\/p>\n<\/p>\n

\"\\text{A<\/p>\n<\/p>\n

\"P(A\\cup<\/p>\n<\/p>\n

\u27a4<\/span>\u53c2\u7167\uff1a<\/strong>\u30a4\u30d9\u30f3\u30c8\u3078\u306e\u53c2\u52a0\u4f8b<\/a><\/div>\n

<\/span>\u30a4\u30d9\u30f3\u30c8\u306e\u4ea4\u5dee\u306e\u516c\u5f0f<\/span><\/h2>\n

\u30a4\u30d9\u30f3\u30c8 A \u3068 B \u306e\u5171\u901a\u90e8\u5206\u306f\u3001\u540c\u6642\u306b A \u3068 B \u306b\u5c5e\u3059\u308b\u3059\u3079\u3066\u306e\u30a4\u30d9\u30f3\u30c8\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u3001\u8a18\u53f7 \u22c2 \u3067\u8868\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30a4\u30d9\u30f3\u30c8 A \u3068 B \u306e\u4ea4\u5dee\u90e8\u5206\u306f A\u22c2B \u3068\u66f8\u304b\u308c\u307e\u3059\u3002<\/p>\n

2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u4ea4\u5dee\u3059\u308b\u78ba\u7387\u306f\u30011 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u306b\u3001\u6700\u521d\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u306b\u3082\u3046 1 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u639b\u3051\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u3057\u305f\u304c\u3063\u3066\u3001 2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u4ea4\u5dee\u78ba\u7387\u306e\u516c\u5f0f\u306f<\/strong>\u3001P(A\u22c2B)=P(A) P(B|A)=P(B) P(A|B) \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/p>\n

\"P(A\\cap<\/p>\n<\/p>\n

\u305f\u3060\u3057\u30012 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u72ec\u7acb\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u3053\u308c\u306f\u3001\u4e00\u65b9\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u306f\u3001\u3082\u3046\u4e00\u65b9\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u304b\u3069\u3046\u304b\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012 \u3064\u306e\u72ec\u7acb\u3057\u305f\u30a4\u30d9\u30f3\u30c8\u306e\u4ea4\u5dee\u78ba\u7387\u306e\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>\n<\/p>\n

\"P(A\\cap<\/p>\n<\/p>\n

\u27a4<\/span>\u53c2\u7167:<\/strong>\u30a4\u30d9\u30f3\u30c8\u306e\u4ea4\u5dee\u306e\u4f8b<\/a><\/div>\n

<\/span>\u30a4\u30d9\u30f3\u30c8\u306e\u5dee\u5206\u306e\u516c\u5f0f<\/span><\/h2>\n

2 \u3064\u306e\u30a4\u30d9\u30f3\u30c8\u9593\u306e\u5dee\u7570\u78ba\u7387\u3068\u306f\u3001\u4e00\u65b9\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u540c\u6642\u306b\u767a\u751f\u305b\u305a\u306b\u4ed6\u65b9\u306e\u30a4\u30d9\u30f3\u30c8\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n

\u3057\u305f\u304c\u3063\u3066\u3001AB \u306e\u6210\u529f\u306e\u5dee\u306e\u78ba\u7387\u306f\u3001\u6210\u529f A \u306e\u78ba\u7387\u304b\u3089\u3001\u6210\u529f A \u3068\u6210\u529f B \u306e\u4ea4\u5dee\u306e\u78ba\u7387\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6210\u529f\u306e\u5dee\u306e\u78ba\u7387\u306e\u516c\u5f0f\u306f<\/strong>\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>\n<\/p>\n

\"P(A-B)=P(A)-P(A\\cap<\/p>\n<\/p>\n

<\/span>\u5168\u78ba\u7387\u5b9a\u7406\u306e\u516c\u5f0f<\/span><\/h2>\n

\u5168\u78ba\u7387\u5b9a\u7406\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u7a7a\u9593\u306e\u4e00\u90e8\u3067\u306f\u306a\u3044\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387\u3092\u3001\u30b5\u30f3\u30d7\u30eb\u7a7a\u9593\u5185\u306e\u3059\u3079\u3066\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u304b\u3089\u8a08\u7b97\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u6cd5\u5247\u3067\u3059\u3002<\/p>\n

\u5168\u78ba\u7387\u5b9a\u7406\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u7a7a\u9593\u4e0a\u3067\u30d1\u30fc\u30c6\u30a3\u30b7\u30e7\u30f3\u3092\u5f62\u6210\u3059\u308b\u4e00\u9023\u306e\u30a4\u30d9\u30f3\u30c8 {A 1<\/sub> \u3001A 2<\/sub> \u3001\u2026\u3001A n<\/sub> } \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u30a4\u30d9\u30f3\u30c8 B \u306e\u78ba\u7387\u306f\u305d\u308c\u305e\u308c\u306e\u78ba\u7387\u306e\u7a4d\u306e\u5408\u8a08\u306b\u7b49\u3057\u3044\u3001\u3068\u3044\u3046\u3082\u306e\u3067\u3059\u3002\u30a4\u30d9\u30f3\u30c8 P(A i<\/sub> ) \u3092\u6761\u4ef6\u4ed8\u304d\u78ba\u7387 P(B|A i<\/sub> ) \u3067\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n

\u3057\u305f\u304c\u3063\u3066\u3001\u5408\u8a08\u78ba\u7387\u5b9a\u7406\u306e\u516c\u5f0f\u306f\u6b21<\/strong>\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<\/p>\n

\"\\displaystyle<\/p>\n<\/p>\n

\u27a4<\/span>\u53c2\u7167:<\/strong>\u5168\u78ba\u7387\u5b9a\u7406\u306e\u4f8b<\/a><\/div>\n

<\/span>\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306e\u516c\u5f0f<\/span><\/h2>\n

\u78ba\u7387\u8ad6\u3067\u306f\u3001\u30d9\u30a4\u30ba\u306e\u5b9a\u7406\u306f\u3001\u30a4\u30d9\u30f3\u30c8\u306b\u95a2\u3059\u308b\u5148\u9a13\u7684\u306a\u60c5\u5831\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u3001\u305d\u306e\u30a4\u30d9\u30f3\u30c8\u306e\u78ba\u7387\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u6cd5\u5247\u3067\u3059\u3002<\/p>\n

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