Two cards are randomly drawn with replacement from a well shuffled deck. What is the probability that at least one is a heart? (There are two ways to solve this problem.) Solution We can solve this problem using the binomial distribution p = .25 = probability of pulling a heart. Since the cards are replaced the probability of pulling a certain color does not change after the first card is drawn. n = 2 = total number of cards drawn x = number of hearts drawn P(X >= 1) = 1 - P(X < 1) = 1 - P(X <= 0) = 1 - P(X=0) =.