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(A) Let $X$ be the random variable representing the number of spade cards drawn. Since the cards are drawn with replacement, this follows a binomial d

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$\frac{3}{8}$

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(A) Let $X$ be the random variable representing the number of spade cards drawn. Since the cards are drawn with replacement, this follows a binomial distribution $B(n, p)$ where $n = 2$ and $p = \frac{13}{52} = \frac{1}{4}$.The probability of success (getting a spade) is $p = \frac{1}{4}$ and the probability of failure is $q = 1 - p = \frac{3}{4}$.The variance of a binomial distribution is given by $Var(X) = npq$.Substituting the values: $Var(X) = 2 	imes \frac{1}{4} 	imes \frac{3}{4} = \frac{6}{16} = \frac{3}{8}$.

Two cards are drawn at random one after the other with replacement from a pack of $52$ playing cards. Then the variance of the random variable of the number of spade cards among the drawn cards is

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