A bridge hand is found by taking 13 cards at random and without replacement from
ID: 3070816 • Letter: A
Question
A bridge hand is found by taking 13 cards at random and without replacement from a deck of 52 playing cards. Find the probability of drawing each of the following hands. e)One in which there are 5 spades, 4 hearts, 3 diamonds, and 1 club (b) One in which there are 5 spades, 4 hearts, 2 diamonds, and 2 clubs. (c) One in which there are 5 spades, 4 hearts, 1 diamond, and 3 clubs. (d) Suppose you are dealt 5 cards of one suit, 4 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?Explanation / Answer
13 cards from a deck of 52 can be selected in 52C13 ways
a)
5 spades from 13 spades can be selected in 13C5 ways
4 hearts from 13 hearts can be selected in 13C4 ways
3 diamonds from 13 diamonds can be selected in 13C3 ways
1 club from 13 clubs can be selected in 13C1 way
Required probability = 13C5 * 13C4 * 13C3 * 13C1 / 52C13
= 0.00539
b)
5 spades from 13 spades can be selected in 13C5 ways
4 hearts from 13 hearts can be selected in 13C4 ways
2 diamonds from 13 diamonds can be selected in 13C2 ways
2 club from 13 clubs can be selected in 13C2 way
Required probability = 13C5 * 13C4 * 13C2 * 13C2 / 52C13
= 0.00882
c)
Required probability = 13C5 * 13C4 * 13C1 * 13C3 / 52C13
= 0.00539
d)
No. Probability of getting a split of 2 , 2 is greater
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