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Manhattan GMAT CAT Question #2

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by mdavidm_531 » Tue Jul 12, 2011 8:17 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, for each value from 1 to 6, there are two cards in the deck with that 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?
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by newgmattest » Tue Jul 12, 2011 8:29 pm
https://www.beatthegmat.com/deck-of-cards-t28564.html
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by amit2k9 » Tue Jul 12, 2011 11:48 pm
one can treat this as a sibling pair and solve it.

probability of having at least one pair = 1- probability of having none.

probability of having none = 12/12 * 10/11 * 8/10* 6/9

thus 16/33
hence
1-16/33 = 17/33.
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