Question

find the probability of having 2,3, or 4 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

Let p be the probability of success, p = 0.4.

Pr[2 success] = nC2 * p^2 * (1-p)^3 = 0.346
Pr[3 success] = nC3 * p^3 * (1-p)^2 = 0.230
Pr[4 success] = nC4 * p^4 * (1-p)^1 = 0.077

So, the probability of getting 2, 3, or 4 success, would be 0.356 + 0.230 + 0.077 = 0.663, alternatively, 66.3%.