Suppose a random variable, X, arises from a binomial experiment. If n = 8 and p = 0.31, find the following probabilities using the binomial formula. Round to four decimal places if necessary.
a) Probability of exactly 3 successes
b) Probability of at least 5 successes
c) Probability of at most 2 successes
d) Probability of exactly 6 successes