{"id":3271,"date":"2025-09-24T14:19:20","date_gmt":"2025-09-24T05:19:20","guid":{"rendered":"https:\/\/math-friend.com\/?p=3271"},"modified":"2025-09-24T14:35:30","modified_gmt":"2025-09-24T05:35:30","slug":"%e3%80%90%e6%9d%b1%e4%ba%ac%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%912%e7%ae%b1%e3%81%ab4%e8%89%b2%e3%81%ae%e7%8e%89%e3%81%8c%e6%8f%83%e3%81%86%e7%a2%ba%e7%8e%87%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=3271","title":{"rendered":"\u3010\u6771\u4eac\u5927\u5b66\u5165\u8a66\u30112\u7bb1\u306b4\u8272\u306e\u7389\u304c\u63c3\u3046\u78ba\u7387\u3092\u6c42\u3081\u308b(2009)"},"content":{"rendered":"\n

\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n

\u30b9\u30a4\u30c3\u30c1\u30921\u56de\u62bc\u3059\u3054\u3068\u306b\u8d64, \u9752, \u9ec4, \u767d\u306e\u3044\u305a\u308c\u304b\u306e\u8272\u306e\u7389\u304c1\u500b, \u7b49\u78ba\u7387\\(\\displaystyle\\frac{1}{4}\\)\u3067\u51fa\u3066\u304f\u308b\u6a5f\u68b0\u304c\u3042\u308b. 2\u3064\u306e\u7bb1L\u3068R\u3092\u7528\u610f\u3059\u308b. \u6b21\u306e3\u7a2e\u985e\u306e\u64cd\u4f5c\u3092\u8003\u3048\u308b.
(\u64cd\u4f5cA) 1\u56de\u30b9\u30a4\u30c3\u30c1\u3092\u62bc\u3057, \u51fa\u3066\u304d\u305f\u7389\u3092L\u306b\u5165\u308c\u308b.
(\u64cd\u4f5cB) 1\u56de\u30b9\u30a4\u30c3\u30c1\u3092\u62bc\u3057, \u51fa\u3066\u304d\u305f\u7389\u3092R\u306b\u5165\u308c\u308b.
(\u64cd\u4f5cC) 1\u56de\u30b9\u30a4\u30c3\u30c1\u3092\u62bc\u3057, \u51fa\u3066\u304d\u305f\u7389\u3068\u540c\u3058\u8272\u306e\u7389\u304c, L\u306b\u306a\u3051\u308c\u3070\u305d\u306e\u7389\u3092L\u306b\u5165\u308c, L\u306b\u3042\u308c\u3070\u305d\u306e\u7389\u3092R\u306b\u5165\u308c\u308b.
\u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. \u305f\u3060\u3057, \u3044\u305a\u308c\u306e\u554f\u3044\u3082\u6700\u521dL\u3068R\u306f\u7a7a\u3067\u3042\u308b\u3068\u3059\u308b.
(1) \u64cd\u4f5cA\u30925\u56de\u884c\u3044, \u3055\u3089\u306b\u64cd\u4f5cB\u30925\u56de\u884c\u3046. \u3053\u306e\u3068\u304dL\u306b\u3082R\u306b\u30824\u8272\u3059\u3079\u3066\u306e\u7389\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\\(P_1\\)\u3092\u6c42\u3081\u3088.
(2) \u64cd\u4f5cC\u30925\u56de\u884c\u3046. \u3053\u306e\u3068\u304dL\u306b4\u8272\u3059\u3079\u3066\u306e\u7389\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\\(P_2\\)\u3092\u6c42\u3081\u3088.
(3) \u64cd\u4f5cC\u309210\u56de\u884c\u3046. \u3053\u306e\u3068\u304dL\u306b\u3082R\u306b\u30824\u8272\u3059\u3079\u3066\u306e\u7389\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\u3092\\(P_3\\)\u3068\u3059\u308b.\\(\\displaystyle\\frac{P_3}{P_1}\\)\u3092\u6c42\u3081\u3088.
(2009 \u6771\u4eac\u5927\u5b66 \u6587\u7cfb [3])<\/span><\/p>\n\n\n\n

\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n

\n

(1) \u307e\u305a, \u64cd\u4f5cA\u30925\u56de\u884c\u3044, L\u306b4\u8272\u3059\u3079\u3066\u306e\u7389\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\u3092\u6c42\u3081\u308b. 5\u56de\u306e\u64cd\u4f5c\u30675\u500b\u306e\u7389\u304c\u51fa\u3066\u304f\u308b\u306e\u3067, \u3069\u308c\u304b1\u8272\u306e\u7389\u306f2\u56de\u51fa\u3066\u304f\u308b\u3053\u3068\u306b\u306a\u308b. 2\u500b\u51fa\u3066\u304f\u308b\u7389\u306e\u8272\u306e\u9078\u3073\u65b9\u304c\\(4\\)\u901a\u308a, \u305d\u306e\u5404\u3005\u306b\u5bfe\u3057\u3066\u7389\u306e\u53d6\u308a\u51fa\u3059\u9806\u756a\u306e\u4e26\u3079\u65b9\u304c\\(\\displaystyle\\frac{5!}{2!}\\)\u901a\u308a, \u6307\u5b9a\u3055\u308c\u305f\u9806\u756a\u3067\u6307\u5b9a\u3055\u308c\u305f\u8272\u306e\u7389\u304c\u51fa\u3066\u304f\u308b\u78ba\u7387\u304c\\(\\displaystyle\\left(\\frac{1}{4}\\right)^5\\)\u306a\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f,$$
4\\times\\frac{5!}{2!}\\times \\left(\\frac{1}{4}\\right)^5 = \\frac{15}{64}
$$\u3068\u306a\u308b.

\u64cd\u4f5cB\u30925\u56de\u884c\u3063\u305f\u3068\u304d\u306b, R\u306b4\u8272\u3059\u3079\u3066\u306e\u7389\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\u3082\u540c\u3058\u304f\\(\\displaystyle\\frac{15}{64}\\)\u3067\u3042\u308a, \u3053\u306e2\u3064\u306f\u72ec\u7acb\u306a\u306e\u3067, \\(P_1\\)\u306f\u3053\u306e2\u3064\u306e\u78ba\u7387\u306e\u7a4d\u3068\u306a\u308a,$$
P_1= \\frac{15}{64}\\times \\frac{15}{64}=\\frac{225}{4096}
$$\u3067\u3042\u308b.<\/p>\n\n\n\n

(2) \u64cd\u4f5cC\u306fL\u306b\u51fa\u3066\u304d\u305f\u7389\u306e\u8272\u304c\u65e2\u306b\u5165\u3063\u3066\u3044\u305f\u3089\u305d\u306e\u7389\u3092R\u306b\u5165\u308c\u308b\u3068\u3044\u3046\u3060\u3051\u3067\u3042\u308a, \u64cd\u4f5cC\u30925\u56de\u884c\u3063\u3066L\u306b4\u8272\u3059\u3079\u3066\u306e\u7389\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\u306f, \u64cd\u4f5cA\u30925\u56de\u884c\u3063\u3066L\u306b4\u8272\u3059\u3079\u3066\u306e\u7389\u304c\u5165\u3063\u3066\u3044\u308b\u78ba\u7387\u3068\u540c\u3058\u3067\u3042\u308b. \u3088\u3063\u3066(1)\u304b\u3089\u305d\u306e\u78ba\u7387\u306f, \\(\\displaystyle \\frac{15}{64}\\)\u3067\u3042\u308b.<\/p>\n\n\n\n

(3) \u6c42\u3081\u308b\u78ba\u7387\u306f10\u56de\u30b9\u30a4\u30c3\u30c1\u3092\u6559\u3057\u3066, \u5404\u82722\u500b\u305a\u3064\u7389\u304c\u51fa\u3066\u304f\u308b\u78ba\u7387\u3068\u540c\u3058\u3067\u3042\u308b. 10\u56de\u30b9\u30a4\u30c3\u30c1\u3092\u62bc\u3059\u4e2d\u3067, 10\u56de\u4e2d8\u56de\u306f\u5404\u8272\u304c2\u500b\u305a\u3064\u51fa\u3066\u304f\u308b\u306e\u3067, \u5c11\u306a\u304f\u3068\u30821\u8272\u306f3\u56de\u4ee5\u4e0a\u51fa\u3066\u304f\u308b\u306e\u3067\u3001\u6b8b\u308a\u306e2\u500b\u306e\u7389\u306e\u8272\u306b\u95a2\u3057\u3066\u5834\u5408\u5206\u3051\u3092\u884c\u3046.

\u2460 4\u8272\u306e\u3046\u3061\u3069\u308c\u304b1\u8272\u304c4\u56de\u51fa\u3066, \u6b8b\u308a\u306e3\u8272\u304c2\u56de\u305a\u3064\u51fa\u308b\u5834\u5408
4\u56de\u51fa\u3066\u304f\u308b\u7389\u306e\u9078\u3073\u65b9\u304c\\(4\\)\u901a\u308a, \u305d\u306e\u5404\u3005\u306b\u5bfe\u3057\u3066\u7389\u306e\u53d6\u308a\u51fa\u3059\u9806\u756a\u306e\u4e26\u3079\u65b9\u304c\\(\\displaystyle\\frac{10!}{4!2!2!2!}\\)\u901a\u308a, \u6307\u5b9a\u3055\u308c\u305f\u9806\u756a\u3067\u6307\u5b9a\u3055\u308c\u305f\u8272\u306e\u7389\u304c\u51fa\u3066\u304f\u308b\u78ba\u7387\u304c\\(\\displaystyle\\left(\\frac{1}{4}\\right)^{10}\\)\u306a\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f,$$
4\\times \\frac{10!}{4!2!2!2!}\\times \\left(\\frac{1}{4}\\right)^{10}
$$\u3068\u306a\u308b.

\u2461 4\u8272\u306e\u3046\u3061\u3069\u308c\u304b2\u8272\u304c3\u56de\u305a\u3064\u51fa\u3066, \u6b8b\u308a\u306e2\u8272\u304c2\u56de\u305a\u3064\u51fa\u308b\u5834\u5408
3\u56de\u51fa\u3066\u304f\u308b\u7389\u306e\u9078\u3073\u65b9\u304c\\({}_4\\mathrm{C}_2\\)\u901a\u308a, \u305d\u306e\u5404\u3005\u306b\u5bfe\u3057\u3066\u7389\u306e\u53d6\u308a\u51fa\u3059\u9806\u756a\u306e\u4e26\u3079\u65b9\u304c\\(\\displaystyle\\frac{10!}{3!3!2!2!}\\)\u901a\u308a, \u6307\u5b9a\u3055\u308c\u305f\u9806\u756a\u3067\u6307\u5b9a\u3055\u308c\u305f\u8272\u306e\u7389\u304c\u51fa\u3066\u304f\u308b\u78ba\u7387\u304c\\(\\displaystyle\\left(\\frac{1}{4}\\right)^{10}\\)\u306a\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f,$$
{}_4\\mathrm{C}_2\\times \\frac{10!}{3!3!2!2!}\\times \\left(\\frac{1}{4}\\right)^{10}
$$\u3068\u306a\u308b.

\u2460, \u2461\u306f\u6392\u53cd\u306a\u306e\u3067\\(P_3\\)\u306f\u3053\u306e2\u3064\u306e\u78ba\u7387\u306e\u548c\u3068\u306a\u308b\u304b\u3089,$$
4\\times \\frac{10!}{4!2!2!2!}\\times \\left(\\frac{1}{4}\\right)^{10}+{}_4\\mathrm{C}_2\\times \\frac{10!}{3!3!2!2!}\\times \\left(\\frac{1}{4}\\right)^{10} = \\frac{10!}{2^{24}}
$$\u3068\u306a\u308b\u304b\u3089,$$
\\frac{P_3}{P_1}=\\frac{10!}{2^{24}}\\times \\frac{2^{12}}{225}=\\frac{63}{16}
$$\u3068\u306a\u308b.<\/p>\n<\/div><\/div>\n\n\n\n

youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n