求教一题数学题

songxiantan · 发表于 2009-8-18 06:44:00

这是我做Manhanttan Gmat模拟考试时遇到的一提数学题,请CD的高人指点一下.谢谢

Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.

Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?

	8/33
		62/165
		17/33
		103/165
		25/33

xuhuixin · 发表于 2009-8-18 12:18:00

我感觉是C

(C6/2+C2/1*C6/1*C5/1*C4/1)/C12/4=(14+240)/495=17/33，不知道对不对

但是还没想出来用反面怎么做。

edmundshi · 发表于 2009-8-18 14:20:00

它的对立事件就是：

Bill finds no pair of cards that have the same value

要想抽出来每张牌的面额都不同，可以把2个面额相同的牌看作一组，从6组面额都不相同的牌中选4张有C(4,6)种方法，每组相同面额有两个不同的牌可以选择，所以总共有(2^4)*C(4,6)种取法

从12张牌里取出4张共有C(4,12)种取法

所以该事件的概率为：[(2^4)*C(4,6)]/C(4,12)=16/33

其对立事件(Bill finds at least one pair of cards that have the same value)的概率是：1-16/33=17/33

选C

weekend1988 · 发表于 2009-8-18 18:06:00

同意楼上解法，非常正确！

求教一题数学题

求教一题数学题

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