Question 1010865: I am solving this problem:
Suppose that you take all of the black cards out of a standard deck of 52 cards and throughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 2 cards, one at a time, without replacement, and record whether each card picked is a face card (king, queen, jack) or not a face card.
I would like to know: the probability that exactly one of the two cards picked is a face card, given that at least one card is a face card?
I know this is a conditional probability, but I am unsure how to go about solving because I don't know whether to treat the first pick as a face card, the second pick as a face card, or both.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose that you take all of the black cards out of a standard deck of 52 cards and throughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 2 cards, one at a time, without replacement, and record whether each card picked is a face card (king, queen, jack) or not a face card.
I would like to know: the probability that exactly one of the two cards picked is a face card, given that at least one card is a face card?
I know this is a conditional probability, but I am unsure how to go about solving because I don't know whether to treat the first pick as a face card, the second pick as a face card, or both.
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P(face|face) = P(face and face)/P(face)
# of ways to get face and face:: 6*5
# of random pairs = 26C2 = 13*25 = 325
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P(face|face) = (30/325)/(6/26) = (30*26)/(325*6) = 0.4
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Cheers,
Stan H.
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