10把鑰匙 - 拼圖

By Lily
at 2009-09-03T10:09
at 2009-09-03T10:09
Table of Contents
※ 引述《EIORU ()》之銘言:
: 眼前有三個已上鎖的盒子
: 分別裝著1,3,5把鑰匙
: 加上手中持有1把鑰匙
: 旁邊有一扇上鎖的門
: 已知盒子和門的鑰匙一定在這10把內
: 請問能夠打開門的機率為何?
第一種情況,手上那把剛好可以開門
機率 = 1/10
第二種情況,只要開一個盒子就好:
譬如說,你手上有第1個盒子的鑰匙,第1個盒子內有門的鑰匙
此部份的機率 = (1/10)*(1/9)+(1/10)*(3/9)+(1/10)*(5/9) = 1/10
第三種情況,要開兩個盒子:
譬如說,你手上有第1個盒子的鑰匙,第1個盒子內有第2個盒子的鑰匙,門的鑰匙在第2個
盒子內
此部份的機率 = (1/10)*(1/9)*(3/8)*2+(1/10)*(1/9)*(5/8)*2+(1/10)*(3/9)*(5/8)*2
= 23/360
第四種情況,要開三個盒子:
譬如說,你手上有第1個盒子的鑰匙,第1個盒子內有第2個盒子的鑰匙,第2個盒子內有
第3個盒子的鑰匙,門的鑰匙在第3個盒子內
此部份的機率 = (1/10)*(1/9)*(3/8)*(5/7)*6 = 1/56
(1/10)+(1/10)+(23/360)+(1/56) = 71/252 --------#Ans
--
: 眼前有三個已上鎖的盒子
: 分別裝著1,3,5把鑰匙
: 加上手中持有1把鑰匙
: 旁邊有一扇上鎖的門
: 已知盒子和門的鑰匙一定在這10把內
: 請問能夠打開門的機率為何?
第一種情況,手上那把剛好可以開門
機率 = 1/10
第二種情況,只要開一個盒子就好:
譬如說,你手上有第1個盒子的鑰匙,第1個盒子內有門的鑰匙
此部份的機率 = (1/10)*(1/9)+(1/10)*(3/9)+(1/10)*(5/9) = 1/10
第三種情況,要開兩個盒子:
譬如說,你手上有第1個盒子的鑰匙,第1個盒子內有第2個盒子的鑰匙,門的鑰匙在第2個
盒子內
此部份的機率 = (1/10)*(1/9)*(3/8)*2+(1/10)*(1/9)*(5/8)*2+(1/10)*(3/9)*(5/8)*2
= 23/360
第四種情況,要開三個盒子:
譬如說,你手上有第1個盒子的鑰匙,第1個盒子內有第2個盒子的鑰匙,第2個盒子內有
第3個盒子的鑰匙,門的鑰匙在第3個盒子內
此部份的機率 = (1/10)*(1/9)*(3/8)*(5/7)*6 = 1/56
(1/10)+(1/10)+(23/360)+(1/56) = 71/252 --------#Ans
--
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