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In a certain game, you pick a card from a standard deck of

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In a certain game, you pick a card from a standard deck of [#permalink] New post 20 Dec 2012, 18:10
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In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws did it take before the person picked a heart and won. What is the probability that there will be at least three draws involved in a win, i.e. someone picking her first heart on the third draw or later?

(A) 1/2
(B) 9/16
(C) 11/16
(D) 13/16
(E) 15/16


For a full discussion of this question and of "at least" probability question in general, see:
http://magoosh.com/gmat/2012/gmat-math- ... -question/
[Reveal] Spoiler: OA

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Re: In a certain game, you pick a card [#permalink] New post 20 Dec 2012, 21:22
In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure how many draws did it take before the person picked a heart and won. What is the probability that there will be at least three draws involved in a win, i.e. someone picking her first heart on the third draw or later?
(A) 1/2
(B) 9/16
(C) 11/16
(D) 13/16
(E) 15/16


Probability of picking a heart on any draw = 1/4
Probability of NOT picking a heart on the first draw AND on the second draw = [1-(1/4)] X [1-(1/4)] = 3/4 X 3/4 = 9/16

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Re: In a certain game, you pick a card   [#permalink] 20 Dec 2012, 21:22
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