SOLUTION: Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a heart?

Question 921516: Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a heart?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Three cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the third card drawn is a heart?
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Patterms:: heart/heart/heart OR notheart/heart/heart ; heart/notheart/heart
OR notheart/notheart/heart
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Counting success::
heart/heart/heart::: 4C3 = 4 ways
nothear/heart/heart:: 48*47*4 ways
heart/hotheart/heart:: 4*48*3 ways
notheart/notheart/heart:: 48*47*4 ways
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Total # of ways to succeed 4 + 2(4*48*47) + 12*48 = 5092
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Total # of sets of 3 cards:: 52C3 = 22100
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P(condition) = 5092/22100
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Cheers,
Stan H.
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