Suppose that the probability is 0.8 that any given person will believe a tale about life after death. What is the probability that the sixth person to hear this tale is the fourth one to believe it

1. Supposethat the probabilityis 0.8 that any given person
will believe a tale about life after death. What is the
probabilitythat the sixth person to hear this tale is the
fourth one to believe it?
Solution
K = 4
p = 0.8
q = 0.2
x = 6
NegativeBinomial Distribution is
𝑃(𝑋 = 𝑥) = (
𝑥 − 1
𝑘 − 1
) 𝑝𝑘
𝑞𝑥−𝑘
𝑃(𝑋 = 6) = (
6 − 1
4 − 1
) (0.8)6
(0.2)6−4
𝑃(𝑋 = 6) = 0.1049