Question 129456: Suppose that you take all of the black cards out of a standard deck of 52 cards and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
a.) What is the probability that none of the 3 cards picked in this way is a face card?
b.) what is the probability that exactly one of the three cards picked is a face card?
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 thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
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There are 6 face-cards in the half-deck.
There are 20 non face-cards in the half-deck.
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a.) What is the probability that none of the 3 cards picked in this way is a face card?
P(3 non face) = 20C3/26C3 = 1140/2600=0.43846...
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b.) what is the probability that exactly one of the three cards picked is a face card?
P(picking one face card) = 6/26= 3/13
P(picking one face in picking three) = 3C1(3/13)(10/13)^2 = 0.4096...
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Cheers,
Stan H.
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