Question

Consider the following binomial experiment. The probability that a green jelly bean is chosen at random from a large package of jelly beans is ¹⁄₄ . If Sally chooses 12 jelly beans, what is the probability that at most 2 will be green jelly beans?

Answer 1

Here, n = 12, p = 0.25, (1 - p) = 0.75 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 2).
P(X <= 2) = (12C0 * 0.25^0 * 0.75^12) + (12C1 * 0.25^1 * 0.75^11) + (12C2 * 0.25^2 * 0.75^10)
P(X <= 2) = 0.0317 + 0.1267 + 0.2323

P(X <= 2) = 0.3907