Take into account the English deck which consists of 52 cards, divided into 4 suits made up of 13 cards each. If 13 cards are dealt (bridge hand): a) How many bridge hands containing 4 spades, 6 diamonds, 1 club and 2 hearts are possible? b) What is the probability of getting a bridge hand that contains 6 diamonds and 3 hearts?
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- Number of ways to choose 4 spades from 13: \( \binom{13}{4} \) - Number of ways to choose 6 diamonds from 13: \( \binom{13}{6} \) - Number of ways to choose 1 club from 13: \( \binom{13}{1} \) - Number of ways to choose 2 hearts from 13: \( \binom{13}{2} \) - Show more…
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1.2-13. A bridge hand is found by taking 13 cards at random and without replacement from a deck of 52 play-ing cards. Find the probability of drawing each of the following hands. (a) One in which there are five spades, four hearts, three diamonds, and one club. (b) One in which there are five spades, four hearts, two diamonds, and two clubs. (c) One in which there are five spades, four hearts, one diamond, and three clubs. (d) Suppose you are dealt five cards of one suit, four cards of another. Would the probability of having the other suits split 3 and 1 be greater than the probability of having them split 2 and 2?
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Find the probability of being dealt a bridge hand of 13 cards containing 5 spades, 2 hearts, 3 diamonds, and 3 clubs.
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Compute the probability of being dealt at random and without replacement a 13 -card bridge hand consisting of: (a) 6 spades, 4 hearts, 2 diamonds, and 1 club; (b) 13 cards of the same suit.
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