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标题: 求教一题数学题 [打印本页]

作者: besttys 时间: 2009-12-24 20:27 标题: 求教一题数学题

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

作者: lixinli 时间: 2009-12-25 07:03

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。

作者: antiquarks 时间: 2009-12-26 06:52

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

作者: swinerton 时间: 2009-12-28 06:57

同意楼上解法，非常正确！

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