{"id":225,"date":"2011-12-03T00:20:24","date_gmt":"2011-12-02T15:20:24","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=225"},"modified":"2021-10-30T10:00:14","modified_gmt":"2021-10-30T01:00:14","slug":"wsr200903","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr200903\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52009\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u30c8\u30e9\u30f3\u30d7\u306e\u30cf\u30fc\u30c8\u3068\u30b9\u30da\u30fc\u30c9\u306e \\(1\\) \u304b\u3089 \\(10\\) \u307e\u3067\u306e\u30ab\u30fc\u30c9\u304c \\(1\\) \u679a\u305a\u3064\u7dcf\u8a08 \\(20\\) \u679a\u3042\u308b.\r\n\\(i = 1, 2, \\cdots , 10\\) \u306b\u5bfe\u3057\u3066, \u756a\u53f7 \\(i\\) \u306e\u30cf\u30fc\u30c8\u3068\u30b9\u30da\u30fc\u30c9\u306e\u30ab\u30fc\u30c9\u306e\u7d44\u3092\u7b2c \\(i\\) \u5bfe\u3068\u3088\u3076\u3053\u3068\u306b\u3059\u308b.\r\n\\(20\\) \u679a\u306e\u30ab\u30fc\u30c9\u306e\u4e2d\u304b\u3089 \\(4\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u7121\u4f5c\u70ba\u306b\u53d6\u308a\u51fa\u3059. \u53d6\u308a\u51fa\u3055\u308c\u305f \\(4\\) \u679a\u306e\u30ab\u30fc\u30c9\u306e\u4e2d\u306b\u7b2c \\(i\\) \u5bfe\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3068\u3044\u3046\u4e8b\u8c61\u3092 \\(A _ i\\) \u3067\u8868\u3059\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u4e8b\u8c61 \\(A _ 1\\) \u304c\u8d77\u3053\u308b\u78ba\u7387 \\(P(A _ 1)\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u78ba\u7387 \\(P( A _ 1 \\cap A _ 2 )\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u78ba\u7387 \\(P( A _ 1 \\cup A _ 2 \\cup A _ 3 )\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  4. (4)<\/strong>\u3000\u53d6\u308a\u51fa\u3055\u308c\u305f \\(4\\) \u679a\u306e\u30ab\u30fc\u30c9\u306e\u4e2d\u306b\u7b2c \\(1\\) \u5bfe, \u7b2c \\(2\\) \u5bfe, \u7b2c \\(3\\) \u5bfe, \u7b2c \\(4\\) \u5bfe, \u7b2c \\(5\\) \u5bfe, \u7b2c \\(6\\) \u5bfe\u306e\u4e2d\u306e\u5c11\u306a\u304f\u3068\u3082 \\(1\\) \u3064\u304c\u542b\u307e\u308c\u308b\u78ba\u7387\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

    \\[\\begin{align}\r\nP( A _ 1 ) & = \\dfrac{{} _ {18} \\text{C} {} _ 2}{{} _ {20} \\text{C} {} _ 4} = \\dfrac{\\frac{18 \\cdot 17}{2!}}{\\frac{20 \\cdot 19 \\cdot 18 \\cdot 17}{4!}} \\\\\r\n& = \\dfrac{9 \\cdot 17}{15 \\cdot 19 \\cdot 17} = \\underline{\\dfrac{3}{95}}\r\n\\end{align}\\]\r\n

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

    \\[\r\nP( A _ 1 \\cap A _ 2 ) = \\dfrac{1}{{} _ {20} \\text{C} {} _ 4} = \\underline{\\dfrac{1}{4845}}\r\n\\]\r\n

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

    \u76f8\u7570\u306a\u308b \\(1\\) \u4ee5\u4e0a \\(10\\) \u4ee5\u4e0b\u306e\u81ea\u7136\u6570 \\(i, j, k\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\nP( A _ i ) = P( A _ 1 ) & = \\dfrac{3}{95} , \\\\\r\nP( A _ i \\cap A _ j ) = P( A _ 1 \\cap A _ 2 ) & = \\dfrac{1}{4845} , \\\\\r\nP( A _ i \\cap A _ j \\cap A _ k) & = 0\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nP( A _ 1 & \\cup A _ 2 \\cup A _ 3 ) \\\\\r\n& = P( A _ 1 ) +P( A _ 2 ) +P( A _ 3 ) \\\\\r\n& \\qquad -P( A _ 1 \\cap A _ 2 ) -P( A _ 1 \\cap A _ 3 ) -P( A _ 2 \\cap A _ 3 ) \\\\\r\n& = 3 \\cdot \\dfrac{3}{95} -3 \\cdot \\dfrac{1}{4845} = 3 \\cdot \\dfrac{9 \\cdot 17 -1}{15 \\cdot 17 \\cdot 19} \\\\\r\n& = \\dfrac{152}{5 \\cdot 17 \\cdot 19} = \\underline{\\dfrac{8}{85}}\r\n\\end{align}\\]\r\n

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

    (3)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u308c\u3070, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\\begin{align}\r\nP( A _ 1 \\cup A _ 2 \\cup A _ 3 & \\cup A _ 4 \\cup A _ 5 \\cup A _ 6 ) \\\\\r\n& = 6 \\cdot \\dfrac{3}{95} -{} _ 6 \\text{C} {} _ 2 \\cdot \\dfrac{1}{4845} \\\\\r\n& = \\dfrac{6 \\cdot 9 \\cdot 17 -15}{15 \\cdot 17 \\cdot 19} =\\dfrac{301}{5 \\cdot 17 \\cdot 19} \\\\\r\n& = \\underline{\\dfrac{301}{1615}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u30c8\u30e9\u30f3\u30d7\u306e\u30cf\u30fc\u30c8\u3068\u30b9\u30da\u30fc\u30c9\u306e \\(1\\) \u304b\u3089 \\(10\\) \u307e\u3067\u306e\u30ab\u30fc\u30c9\u304c \\(1\\) \u679a\u305a\u3064\u7dcf\u8a08 \\(20\\) \u679a\u3042\u308b. \\(i = 1, 2, \\cdots , 10\\) \u306b\u5bfe\u3057\u3066, \u756a\u53f7 \\(i\\) \u306e\u30cf\u30fc\u30c8\u3068\u30b9 … \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":[36],"tags":[147,15],"class_list":["post-225","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2009","tag-waseda_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/225","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=225"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/225\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=225"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=225"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}