{"id":892,"date":"2020-06-03T11:00:00","date_gmt":"2020-06-03T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=892"},"modified":"2020-06-06T22:19:46","modified_gmt":"2020-06-06T13:19:46","slug":"conditional-probability","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/conditional-probability","title":{"rendered":"\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3010\u610f\u5473\u3068\u6c42\u3081\u65b9\u3092\u89e3\u8aac\u3011"},"content":{"rendered":"\n

\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u4e2d\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n

\u3000\u78ba\u7387\u3092\u6c42\u3081\u308b\u3068\u304d\u3001\u4e8b\u524d\u306b\u4f55\u3089\u304b\u306e\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002
\u3000\u5177\u4f53\u7684\u306b\u3001\u3042\u305f\u308a\u5165\u308a\u306e\u304f\u3058\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002\u81ea\u5206\u306e\u524d\u306e\u4eba\u304c[\u30cf\u30ba\u30ec]\u304f\u3058\u3092\u5f15\u3044\u305f\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u81ea\u5206\u304c[\u30a2\u30bf\u30ea]\u304f\u3058\u3092\u5f15\u304f\u78ba\u7387\u304c\u4e0a\u304c\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u524d\u306e\u4eba\u304c\u5f15\u3044\u305f\u304f\u3058\u306e\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u304b\u3089\u3001\u81ea\u5206\u304c[\u30a2\u30bf\u30ea]\u3092\u5f15\u304f\u78ba\u7387\u304c\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u306a\u3044\u3068\u304d\u3068\u306f\u7570\u306a\u3063\u305f\u3082\u306e\u306b\u306a\u308a\u307e\u3059\u3002
\u3000\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u4e8b\u524d\u306b\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u4e0b\u3067\u306e\u3001\u78ba\u7387\u306e\u5c0e\u304d\u65b9\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n

\u6761\u4ef6\u4ed8\u304d\u78ba\u7387<\/h3>\n\n\n\n
<\/div>

\u65e9\u901f\u3001\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\uff01<\/p>

<\/div><\/div><\/div>\n\n\n\n
\u6761\u4ef6\u4ed8\u304d\u78ba\u7387(conditional probability)<\/strong><\/div>\n
\u6761\u4ef6\u4ed8\u304d\u78ba\u7387<\/strong>\u3068\u306f\u3001\u4e8b\u8c61\\(A\\)\u304c\u8d77\u3053\u308b\u78ba\u7387\u3092\u4e8b\u8c61\\(B\\)\u3067\u6761\u4ef6\u4ed8\u3051\u305f\u3082\u306e\u3067\u3042\u308a\u3001\u8a18\u53f7$$\\mathrm{P}(A|B)$$\u3067\u8868\u3057\u307e\u3059\u3002\u307e\u305f\u4e8b\u8c61\\(A\\)\u306e\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306f\u4e8b\u8c61\\(B\\)\u306e\u78ba\u7387\u304c\u4e0e\u3048\u3089\u308c\u305f\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u306e\u3067$$\\mathrm{P}(A|B)=\\frac{\\mathrm{P}(A\\cap B)}{\\mathrm{P}(B)}$$\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/div>\n

 <\/p>\n\n\n\n

\u203b\u3000\u6e2c\u5ea6\u8ad6\u7684\u306b\u5b9a\u7fa9\u3059\u308b\u3068\u9762\u5012\uff08\u6e96\u5099\u304a\u3088\u3073\u5fc5\u8981\u306a\u6570\u5b66\u306e\u77e5\u8b58\u91cf\u304c\u591a\u3044\uff09\u306a\u5185\u5bb9\u306b\u306a\u308b\u306e\u3067\u3001\u672c\u30d6\u30ed\u30b0\u3067\u306f\u30b3\u30c1\u30e9\u3067\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n\n\n\n

\u78ba\u7387\u306e\u4e57\u6cd5\u5b9a\u7406<\/strong><\/div>\n
\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306e\u5b9a\u7fa9\u304b\u3089\u6b21\u306e\u3088\u3046\u306a\u78ba\u7387\u306e\u4e57\u6cd5\u5b9a\u7406\u3068\u3044\u3046\u3082\u306e\u304c\u5f97\u3089\u308c\u307e\u3059\u3002$$\\mathrm{P}(A\\cap B)=\\mathrm{P}(A|B)\\mathrm{P}(B)$$<\/div>\n

 <\/p>\n\n\n\n

<\/div>

\u5177\u4f53\u4f8b\u3092\u7528\u3044\u3066\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\uff01<\/p>

<\/div><\/div><\/div>\n\n\n\n
\u30002\u3064\u306e\u5de5\u5834A\u3001B\u3067\u4f5c\u3089\u308c\u308b\u88fd\u54c1\u306b\u3064\u3044\u3066\u4e0d\u826f\u54c1\u304c\u51fa\u308b\u78ba\u7387\u304c\u305d\u308c\u305e\u308c2%\u30015%\u3067\u3042\u308b\u3068\u3059\u308b\u3002\u307e\u305f\u3001\u5de5\u5834A\u304b\u3089\u51fa\u8377\u3055\u308c\u305f\u88fd\u54c1\u304c\u5168\u4f53\u306e3\u5272\u3001\u5de5\u5834B\u304b\u3089\u51fa\u8377\u3055\u308c\u305f\u88fd\u54c1\u304c\u5168\u4f53\u306e7\u5272\u3092\u5360\u3081\u307e\u3059
\u30002\u3064\u306e\u5de5\u5834\u304b\u3089\u4f5c\u3089\u308c\u305f\u88fd\u54c1\u306e\u4e2d\u304b\u30891\u500b\u53d6\u308a\u51fa\u3059\u3068\u304d\u3001\u305d\u308c\u304c\u4e0d\u826f\u54c1\u3067\u3042\u308b\u78ba\u7387\u3092\u6c42\u3081\u306a\u3055\u3044\u3002<\/div>\n\n\n\n

\u53d6\u308a\u51fa\u3057\u305f\u88fd\u54c1\u304c\u5de5\u5834A\u3001B\u3067\u3064\u304f\u3089\u308c\u305f\u3068\u3044\u3046\u4e8b\u8c61\u3092\\(A\u3001B\\)\u3068\u3057\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u53d6\u308a\u51fa\u3057\u305f\u88fd\u54c1\u304c\u4e0d\u826f\u54c1\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u8c61\u3092\\(E\\)\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u554f\u984c\u6587\u304b\u3089\u3001

\\begin{align}
&\\mathrm{P}(A)=0.30,\\ \\ \\ \\mathrm{P}(B)=0.70\\\\
&\\mathrm{P}(E|A)=0.02,\\ \\ \\ \\mathrm{P}(E|B)=0.05
\\end{align}<\/div>
\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u307e\u3059\u3002\u5168\u4e8b\u8c61\u3092\\(\\Omega\\)\u3068\u3057\u3066\u78ba\u7387\u306e\u52a0\u6cd5\u5b9a\u7406\u30fb\u4e57\u6cd5\u5b9a\u7406\u3092\u7528\u3044\u308b\u3068\u3001\u6c42\u3081\u305f\u3044\u78ba\u7387\\(\\mathrm{P}(E)\\)\u306f
\\begin{align}
\\mathrm{P}(E) &= \\mathrm{P}(E\\cap \\Omega) \\\\
&= \\mathrm{P}(E\\cap (A\\cup B))\\\\
&= \\mathrm{P}(E\\cap A)+\\mathrm{P}(E\\cap B) \\\\
&= \\mathrm{P}(A)\\mathrm{P}(E|A)+\\mathrm{P}(B)\\mathrm{P}(E|B)\\\\
&= 0.30\\times 0.02 + 0.70\\times 0.05\\\\
&= 0.041
\\end{align}<\/div>
\u3068\u306a\u308b\u306e\u3067\u3001\u6c42\u3081\u305f\u3044\u78ba\u7387\u306f4.1%<\/span>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u203b\u3000\u78ba\u7387\u306e\u52a0\u6cd5\u5b9a\u7406\u306b\u3064\u3044\u3066\u306f\uff1c\u78ba\u7387\u306e\u5b9a\u7fa9\u306e\u8a18\u4e8b\uff1e<\/a>\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\uff01<\/p>\n\n\n\n

<\/div>

\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u30de\u30b9\u30bf\u30fc\u3059\u308b\u3068\u3001\u78ba\u7387\u3067\u3067\u304d\u308b\u3053\u3068\u304c\u5e83\u304c\u308a\u307e\u3059\u3002\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306f\u30d9\u30a4\u30ba\u7d71\u8a08\u5b66\u306e\u57fa\u790e\u3068\u306a\u308b\u306e\u3067\u3001\u4eba\u5de5\u77e5\u80fd\u3084\u4e88\u6e2c\u3092\u3057\u3066\u3044\u304d\u305f\u3044\u65b9\u306f\u662f\u975e\u3068\u3082\u4f7f\u3044\u3053\u306a\u305b\u308b\u3088\u3046\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>

<\/div><\/div><\/div>\n\n\n\n

\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306e\u307e\u3068\u3081<\/h3>\n\n\n\n

\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306f\u4e8b\u524d\u306b\u60c5\u5831\u304c\u5f97\u3089\u308c\u305f\u4e0b\u3067\u3001\u78ba\u7387\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u3067\u3059\u3002\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u3092\u7528\u3044\u3066\u3001\u78ba\u7387\u306e\u4e57\u6cd5\u5b9a\u7406\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u306f\u30d9\u30a4\u30ba\u7d71\u8a08\u5b66\u306e\u57fa\u790e\u306b\u306a\u308b\u306e\u3067\u3001\u4e88\u6e2c\u3084\u4eba\u5de5\u77e5\u80fd\u306a\u3069\u3092\u52c9\u5f37\u3057\u3066\u3044\u304d\u305f\u3044\u65b9\u306f\u662f\u975e\u3068\u3082\u62bc\u3055\u3048\u3066\u304a\u304d\u305f\u3044\u5206\u91ce\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u4e2d\u5b66\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606 \u3000\u78ba\u7387\u3092\u6c42\u3081\u308b\u3068\u304d\u3001\u4e8b\u524d\u306b\u4f55\u3089\u304b\u306e\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3000\u5177\u4f53\u7684\u306b\u3001\u3042\u305f\u308a\u5165\u308a\u306e\u304f\u3058\u3092 … <\/p>\n","protected":false},"author":1,"featured_media":829,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[54],"tags":[59,55,60],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/135-money-images.jpg","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/892"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=892"}],"version-history":[{"count":14,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/892\/revisions"}],"predecessor-version":[{"id":1066,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/892\/revisions\/1066"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/829"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}