binomial distribution

Question

Find the probability of 2 or 3 successes in 7 trials of a binomial experiment in which the probability of success in any one trial is 42% Round to the nearest tenth of a percent.

Answer 1

Prob{k=2|n=7;p=0.42} + Prob{k=3|n=7;p=0.42}

Answer 2

p = probability of success on a given trial = 0.42

q = probability of failure on a given trial = 1 - 0.42 = 0.58

Probability of 2 or 3 successes out of 7 trials =

₇C₂(0.42)²(0.58)^7-2 + ₇C₃(0.42)³(0.58)^7-3 = 0.5365866 = 53.7%