{"id":279,"date":"2012-01-28T23:35:28","date_gmt":"2012-01-28T14:35:28","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=279"},"modified":"2021-09-10T21:18:23","modified_gmt":"2021-09-10T12:18:23","slug":"tok200803","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok200803\/","title":{"rendered":"\u6771\u5de5\u59272008\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u3044\u3073\u3064\u306a\u30b5\u30a4\u30b3\u30ed\u304c\u3042\u308a, \\(1\\) \u304b\u3089 \\(6\\) \u307e\u3067\u306e\u305d\u308c\u305e\u308c\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u304c \\(\\dfrac{1}{6}\\) \u3068\u306f\u9650\u3089\u306a\u3044\u3068\u3059\u308b.\r\n\u3053\u306e\u30b5\u30a4\u30b3\u30ed\u3092 \\(2\\) \u56de\u3075\u3063\u305f\u3068\u304d\u540c\u3058\u76ee\u304c\u51fa\u308b\u78ba\u7387\u3092 \\(P\\) \u3068\u3057, \\(1\\) \u56de\u76ee\u306b\u5947\u6570, \\(2\\) \u56de\u76ee\u306b\u5076\u6570\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u3092 \\(Q\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(P \\geqq \\dfrac{1}{6}\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b. \u307e\u305f, \u7b49\u53f7\u304c\u6210\u7acb\u3059\u308b\u305f\u3081\u306e\u5fc5\u8981\u5341\u5206\u6761\u4ef6\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\dfrac{1}{4} \\geqq Q \\geqq \\dfrac{1}{2} -\\dfrac{3}{2} P\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\(k \\ ( k =1, 2, \\cdots , 6 )\\) \u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u3092 \\(p _ k\\) \u3068\u304a\u304f.\r\n\\[\\begin{align}\r\np _ 1 +p _ 2 & + \\cdot +p _ 6 =1 , \\\\\r\nP = {p _ 1}^2 & +{p _ 2}^2 + \\cdots +{p _ 6}^2\r\n\\end{align}\\]\r\n\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f\u3088\u308a\r\n\\[\\begin{align}\r\n( 1 \\cdot p _ 1 +1 \\cdot p _ 2 + \\cdots +1 \\cdot p _ 6 )^2 & \\\\\r\n\\leq ( 1^2 +1^2 + \\cdots & + 1^2 ) ( {p _ 1}^2 +{p _ 2}^2 + \\cdots +{p _ 6}^2 ) \\\\\r\n1 & \\leqq 6P \\\\\r\n\\text{\u2234} \\quad P & \\geqq \\dfrac{1}{6}\r\n\\end{align}\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(p _ 1 =p _ 2 = \\cdots =p _ 6 =\\dfrac{1}{6}\\) \u306e\u3068\u304d\u3067\u3042\u308b.<\/p>\r\n

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

    \u5947\u6570\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u3092 \\(q\\) \u3068\u304a\u304f\u3068, \\(0 \\leqq q \\leqq 1\\) .
    \r\n\u5076\u6570\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u306f \\(1-q\\) \u3068\u8868\u305b\u308b\u306e\u3067\r\n\\[\r\nQ = q (1-q) = -\\left( q-\\dfrac{1}{2} \\right)^2 +\\dfrac{1}{4} \\leqq \\dfrac{1}{4} \\quad ... [1]\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(q =\\dfrac{1}{2}\\) \u306e\u3068\u304d.
    \r\n\u6b21\u306b, (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\r\n3P +2Q -1 \\geqq 3 \\cdot \\dfrac{1}{6} +2Q -1 = 2Q -\\dfrac{1}{2} \\quad ... [2]\r\n\\]\r\n\u7b49\u53f7\u304c\u6210\u7acb\u3059\u308b\u3068\u304d, \\(q = p _ 1+p _ 3+p _ 5 = \\dfrac{1}{2}\\) \u306a\u306e\u3067, [1] \u3088\u308a\r\n\\[\\begin{align}\r\n[2] & = 2 \\cdot \\dfrac{1}{4} -1 = 0 \\\\\r\n\\text{\u2234} \\quad Q & \\geqq \\dfrac{1}{2} -\\dfrac{3}{2} P\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\dfrac{1}{4} \\geqq Q \\geqq \\dfrac{1}{2} -\\dfrac{3}{2} P\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u3044\u3073\u3064\u306a\u30b5\u30a4\u30b3\u30ed\u304c\u3042\u308a, \\(1\\) \u304b\u3089 \\(6\\) \u307e\u3067\u306e\u305d\u308c\u305e\u308c\u306e\u76ee\u304c\u51fa\u308b\u78ba\u7387\u304c \\(\\dfrac{1}{6}\\) \u3068\u306f\u9650\u3089\u306a\u3044\u3068\u3059\u308b. \u3053\u306e\u30b5\u30a4\u30b3\u30ed\u3092 \\(2\\) \u56de\u3075\u3063\u305f\u3068\u304d\u540c\u3058\u76ee\u304c\u51fa\u308b\u78ba\u7387\u3092 \\(P\\) \u3068\u3057 … \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":[50],"tags":[141,16],"class_list":["post-279","post","type-post","status-publish","format-standard","hentry","category-toko_2008","tag-toko","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/279","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=279"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/279\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}