Probability of a full house
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4. In one variety of poker, players are dealt five cards from an ordinary deck of 52 cards.
(a) A full house in poker is a hand of five cards of one denomination and 3 cards of another denomination. Find the probability of a player being dealt a full house.
(b) Two pairs is a poker hand containing 2 cards of one denomination, another 2 cards of a second denomination, and a fifth cards of a third dimension. Find the probability of a player being dealt two pairs.
5. Given n marbles where k of the marbles are black and the rest are white, a game is played as follows. You choose two marbles at random, and you win the game if the marbles are of different colors. Prove that for a fixed n, you have the highest probability of winning when k = n/2 (for even values of n) and when k = (n (plus or minus) 1)/2 (for odd values of n).
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Solution Summary
In this solution the probability of a full house is carefully depicted in this solution. Step by step calculations are given, along with explanations.
Solution Preview
Please see the attached document for step by step calculations for both of the questions.
Probability of a full house:
13(■(4@3))12(■(4@2))/((■(52@5)) ...
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