binomial distributions

Question

Find the probability of exactly four successes in five trials of a binomial experiment in which the probability of success is 40% Round to the nearest tenth of a percent.

Answer 1

p = probability of success = 0.40

q = probability of failure = 1 - p = 0.60

Probability of 4 successes in 5 trials = ₅C₄(p⁴)(q^5-4)

= [5! / ((4!)(5-4)!)](0.4)⁴(0.6)¹ = 5(0.01536) = 0.0768 = 7.7%