Question

Suppose that a family has 5 children. Also, suppose that the probability of having a girlis probability that the family has the following children. Find the Exactly 2 girls and 3 boys The probability is Type an integer or a simplified fraction.)

Answer 1

You use the binomial distribution.

P(x) = C(n,x)p^x(1-p)^(n-x) As p = 1/2, 1-p = 1/2 also, so p^x(1-p)^(n-x) = 1/2^x*1/2^(n-x) = 1/2^n

Thus, as n = 5

Thus, P(x) = C(5,x)(1/2)^5 = C(5,x)/2^5 = C(5,x)/32

Then, P(2) = C(5,2)/32 = 5*4/(2*1)/32 = (20/2)/32 = 10/32 = 5/16