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Question

# Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Find the probability distribution of the number of aces.

A
1169
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B
1221
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C
1265
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D
4663
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Solution

## The correct option is A 1169Total no. of cards = 52Total no. of aces = 4P(ace)=452=113P(non−ace)=4852=1213Let X be a random variable, such thatX = no. of aces obtained in 2 draws.Case I:- X = 0 (No aces are obtained)P(X=0)=P(non-ace and non-ace)=P(non−ace)×P(non−ace)=1213×1213=144169Case II:- X = 1 (1 ace is obtained)P(X=1)=P((ace and non-ace) or (non-ace and ace))=(P(non−ace)×P(non−ace))+(P(ace)×P(non−ace))=(1213×113)+(113×1213)=24169Case III:- X = 2 (two aces are obtained)P(X=2)=P(ace and ace)=P(ace)×P(ace)=113×113=1169

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