Question

during a single day at radio station WMZH, the probability that a particular song is plated is 62% what is the probability that this song will be played on at most 2 days out of 6 days round the nearest thousandth

Answer 1

Let X ~ Binomial(n=6, p=0.62). We want P(X ≤ 2):

P(X ≤ 2) = Σ_{k=0}^2 C(6,k) (0.62)^k (0.38)^(6−k)
= (0.38)^6 + 6(0.62)(0.38)^5 + 15(0.62)^2(0.38)^4
≈ 0.003011 + 0.029475 + 0.120229 = 0.152715

Rounded to the nearest thousandth: 0.153.