In a poker game 5 cards are dealt from a standard 52 card de

In a poker game, 5 cards are dealt from a standard 52 card deck that has been well shuffled. You are the only player in this scenario. How many different 5 card hands are possible? What is the probability that you are dealt two pairs? What is the probability that you are dealt a 3 of a kind or 4 of a kind? What is the probability that you are dealt a full house? What is the probability that you are dealt a flush, 3 of a kind, or 4 of a kind? (any type of flush is acceptable)

Solution

Answer to part a)

Number of ways in which 5 cards can be helpd out of 52 = 52C5 = 2598960

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Answer to part b)

P(2 pairs) = 13C2*13C2*26C1 / 52C5 = 13*6*13*6*26 / 2598960 = 0.0609

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Answer to part c)

P(3 of a kind) = 13C3 * 39C2 / 52C5 = 286 * 741 / 2598960 = 0.0815

P(4 of a kind) = 13C4 *39C1 / 52C5 = 143*39 / 2598960 = 0.002146

P(3 or 4) = 0.0815 + 0.002146 = 0.08369

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Answer to part d)

P(full house) = 4* 13C5 / 52 C5 = 4*1287 / 2598960 = 0.001981