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Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let X danote the random variable of number of aces obtained in the two drawn cards. Then, P(X = 1) + P(X = 2) equals A. 25 169 B. 52 169 C. 49 169 D. 24 169 Select the correct answer from above options

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Correct Answer - A Let p=probability of getting an ace in a draw=probability of success and q=probability of not getting an ace in a draw= probability of failure Then, p= 4 52 = 1 13 and q=1-p=1- 1 13 = 12 13 ltbrlt Here, number of trials, n=2 Clearly, X follows binomial distribution with parameter n=2 and p= 1 13 . Now, P(X=x)= 2 Cx( 1 13 )x( 12 13 )2-x,x=0,1,2 ∴P(x=1)+P(X=2) = 2 C1( 1 13 )1( 12 13 )+ 2 C2( 1 13 )2( 12 13 )0 =2( 12 169 )+ 1 169 = 24 169 + 1 169 = 25 169

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