Re: [理工] [機率]-機率導論
※ 引述《winshain (人就是要磨鍊)》之銘言：
: A quiz was administered to four students.Somehow the quizzes got shuffled,
: and the one at the top of the stack was returned to first student
: ,the one below it was returned to the second student,and so on.
: Find the probability that at least one student got his own quiz back.
: 請問各位大大,如何去思考這類的題目呢?
: 是利用配對方式去想比較容易嗎?我想知道各位的想法?謝謝!
利用排容原理去解題~
設Ai為第i個學生拿到自己測驗卷的事件
P(至少一個學生拿到自己測驗卷)=P(A1∪A2∪A3∪A4)
=P(A1)+P(A2)+P(A3)+P(A4)-P(A1A2)-P(A1A3)-P(A1A4)-P(A2A3)-P(A2A4)-P(A3A4)
+P(A1A2A3)+P(A1A2A4)+P(A1A3A4)+P(A2A3A4)-P(A1A2A3A4)
3! 2! 1! 0!
= C(4,1)*── -C(4,2)*── +C(4,3)*── -C(4,4)*──
4! 4! 4! 4!
1 1 1 24-12+4-1 15 5
= 1 - ─ + ─ - ─ = ───── = ── = ──
2 6 24 24 24 8
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