SOLUTION: If you are dealt a 5-card hand (this implies without replacement) from a standard 52-card deck, find the probability of getting a black flush or two pairs. Give answers to six deci

Question 232557: If you are dealt a 5-card hand (this implies without replacement) from a standard 52-card deck, find the probability of getting a black flush or two pairs. Give answers to six decimal points.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If you are dealt a 5-card hand (this implies without replacement) from a standard 52-card deck, find the probability of getting a black flush or two pairs. Give answers to six decimal points.
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These events are mutually exclusive so the probability
is P(black flush) + P(2 pairs)
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# of flushes in one suit: 13C5 = 1287
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there are 2 black suits
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P(black flush) = [2*1287]/52C5 = 2574/2598960 = 2574/2598960 = 0.0009904..
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2 pairs:
Pick two card types: 13C2 = 78 ways
Form a pair: 4C2 = 6
Form a 2nd pair: 4C2 = 6
Pick a 5th card: 11 ways
Pick a suit: 4C1 = 4
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P(2 pairs in hand of 5) = (78*36*11*4)/52C5 = 0.047539...
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P(black flush or 2 pairs in 5 card hand) = the sum = 0.04853...
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Cheers,
Stan H.

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