{"id":162,"date":"2011-12-01T18:19:44","date_gmt":"2011-12-01T09:19:44","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=162"},"modified":"2021-11-04T09:43:33","modified_gmt":"2021-11-04T00:43:33","slug":"htb201005","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201005\/","title":{"rendered":"\u4e00\u6a4b\u59272010\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(n\\) \u3092 \\(3\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3059\u308b.\r\n\u30b5\u30a4\u30b3\u30ed\u3092 \\(n\\) \u56de\u6295\u3052, \u51fa\u305f\u76ee\u306e\u6570\u3092\u305d\u308c\u305e\u308c\u9806\u306b \\(X _ 1 , X _ 2 , \\cdots X _ n\\) \u3068\u3059\u308b. \\(i = 2 , 3 , \\cdots n\\) \u306b\u5bfe\u3057\u3066 \\(X _ i = X _ {i-1}\\) \u3068\u306a\u308b\u4e8b\u8c61\u3092 \\(A _ i\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(A _ 2 , A _ 3 , \\cdots , A _ n\\) \u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u304c\u8d77\u3053\u308b\u78ba\u7387 \\(p _ n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(A _ 2 , A _ 3 , \\cdots , A _ n\\) \u306e\u3046\u3061\u5c11\u306a\u304f\u3068\u3082 \\(2\\) \u3064\u304c\u8d77\u3053\u308b\u78ba\u7387 \\(q _ n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\(A _ 2 , A _ 3 , \\cdots , A _ n\\) \u306e\u3046\u3061, \u3061\u3087\u3046\u3069 \\(k\\) \u500b\uff08 \\(0 \\leqq k \\leqq n\\) \uff09\u304c\u8d77\u3053\u308b\u4e8b\u8c61\u3092 \\(B _ k\\) , \u78ba\u7387\u3092 \\(b _ k\\) \u3068\u304a\u304f.\r\n\\[\r\nb _ 0 = \\dfrac{6 \\cdot 5^{n-1}}{6^n} = \\left( \\dfrac{5}{6} \\right)^{n-1}\r\n\\]\r\n\u984c\u610f\u306e\u4e8b\u8c61\u306f \\(B _ 0\\) \u306e\u4f59\u4e8b\u8c61\u306a\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\np _ n = 1 -b _ 0 = \\underline{1 -\\left( \\dfrac{5}{6} \\right)^{n-1}}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \\[\r\nb _ 1 = \\dfrac{( n-1 ) \\cdot 6 \\cdot 5^{n-2}}{6^n} = \\dfrac{n-1}{6} \\left( \\dfrac{5}{6} \\right)^{n-2}\r\n\\]\r\n\u984c\u610f\u306e\u4e8b\u8c61\u306f \\(B _ 0 \\cup B _ 1\\) \u306e\u4f59\u4e8b\u8c61\u3067, \\(B _ 0 \\cap B _ 1 = \\phi\\) \u306a\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\nq _ n = 1 -b _ 0 -b _ 1 = \\underline{1 - \\dfrac{n+4}{6} \\left( \\dfrac{5}{6} \\right)^{n-2}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u3092 \\(3\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3059\u308b. \u30b5\u30a4\u30b3\u30ed\u3092 \\(n\\) \u56de\u6295\u3052, \u51fa\u305f\u76ee\u306e\u6570\u3092\u305d\u308c\u305e\u308c\u9806\u306b \\(X _ 1 , X _ 2 , \\cdots X _ n\\) \u3068\u3059\u308b. \\(i = 2 , 3 , \\cd … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[46],"tags":[146,14],"class_list":["post-162","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2010","tag-hitotsubashi","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=162"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/162\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}