6 What is the probability that the second daughter of a coup

6. What is the probability that the second daughter of a couple is their fourth child?

Solution

This is a negative binomial distribution problem.

Note that

P(n, x) = C(n-1,x-1) p^x (1-p)^(n-x)

where n = number of trials = 4
x = number of successes = 2
p = probability of success = 0.5

Thus,

P(4, 2) = C(4-1,2-1) 0.5^2 (1-0.5)^(4-2)

= 0.1875 [ANSWER]