Two cards are drawn successively with replacement from fair playing 52 cards. let X denote number of kings obtained when two cards are drawn, then E ( X ^2 )=

Step-by-step solution

Let X represent the number of kings obtained when drawing two cards with replacement from a standard 52-card deck. The probability of drawing a king is P(K) = 4 52 = 1 13 , while the probability of not drawing a king is P(K') = 12 13 . Since the draws are independent, the probability distribution of X is given by: P(X=0) = P(K') P(K') = 12 13 12 13 = 144 169 P(X=1) = P(K)P(K') + P(K')P(K) = 2 1 13 12 13 = 24 169 P(X=2) = P(K) P(K) = 1 13 1 13 = 1 169 These probabilities sum to 144+24+1 169 = 1 , confirming a valid