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MGMAT CAT - 1

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MGMAT CAT - 1

by singh_amit19 » Fri Oct 05, 2007 10:47 pm
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?

A. 8/33

B. 62/165

C. 17/33

D. 103/165

E. 25/33
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by singh_amit19 » Fri Oct 05, 2007 10:48 pm
My approach:

1 - probability of non-similar cards being picked up
= 1- 2 X (6C4/12C4)
= 31 / 33

Why i am wrong???
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by ratindasgupta » Fri Oct 05, 2007 11:41 pm
Here's my approach. (1 - prob of picking no pairs)

The probability of picking the first card is 1.

The prob of picking the second card that is not a pair of the 1st card is 10/11

The prob of picking the 3rd card which is not a pair of the 1st and 2nd card is 8/10

The prob of picking the 4th card that isnt a pair of the 1st or 2nd or 3rd card is 6/9

Hence, prob of picking cards that are not pairs is
1 x 10/11 x 8/10 x 6/9 = 16/33

So prob that at least one pair of cards that have the same value = (1 - 16/33) = 17/33

Answer is C
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