Question 194889: Five cards are drawn from a deck without replacement. The number of aces is counted. Find the expected number of aces.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Five cards are drawn from a deck without replacement. The number of aces is counted. Find the expected number of aces.
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The random varible, X, is a count of the number of acces drawn.
Values of the random variable are 0, 1, 2, 3, 4
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The corresponding probabilities are:
P(X = 0) = 49C5/52C5
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P(X = 1) = [4C1*48C4]/52C5
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P(X = 2) = (4C2*48C3)/52C5
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P(X = 3) = (4C3*48C2)/52C5
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P(x = 4) = (4C4*48C1)/52C5
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To find the expected number of aces drawn, multiply each
X value by its corresponding probability ; then add the
four products.
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Cheers,
Stan H.
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