Question

A study conducted at a certain college shows that 57% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 9 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

Answer 1

Binomial distribution with p = 0.57, q = 1 - p = 1 - 0.57 = 0.43, n = 9
P(X > x) = nCx * p^x * q^(n - x)
P(X ≥ 1) = 1 - P(0)
P(0) = 9C0 * (0.57)^0 * (0.43)^9 = 1 * 1 * 0.0005026

Therefore, the probability that at least one finds a job in his or her chosen field within a year of graduating is 1 - 0.0005026 = 0.9995 or 99.95%