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# In a five card poker hand, if two of your cards are aces, what is the probability of a full house?

Update:

There is no specification of exactly 2 aces.

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- M3Lv 79 years agoBest Answer
by two aces, i take it that it means exactly 2 aces.

n[full house with 2 aces ] = 4c2 *12c1*4c3 = A

n[2 aces] = 4c2*48c3 = B

P[full house | 2 aces] = A/B 48/48c3 = 3/1081 <-------

your AD

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if 3 aces are also allowed, just add

n[full house with 3 aces] = 4c3*12c1*4c2 to = A"

n[3 aces] = 4c3*48c2 = B"

and compute (A+A") /(B+B")

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