Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........

Step-by-step solution

Probability of drawing a club card, p = 13 52 = 1 4 Probability of not drawing a club card, q = 1 - p = 3 4 Number of trials, n = 4 Number of successes, r = 2 Using binomial distribution, P(X = r) = ^ n C_ r p^ r q^ n-r P(X = 2) = ⁴C₂ ( 1 4 )² ( 3 4 )² P(X = 2) = 6 1 16 9 16 P(X = 2) = 54 256 = 27 128 Answer: 27 128