Question

Suppose that in 4-child families, each child is equally likely to be a boy or a girl, independently of the others. Which would then be more common, 4-child families with 2 boys and 2 girls, or 4 child families with different numbers of boys and girls? What would be the relative frequencies? (Detailed answer using binomial distribution)

Answer 1

Solution:-

The relative frequencies is 0.60.

The 4-child families with 2 boys and 2 girls will be less common as comparative to 4 child families with different numbers of boys and girls.

Boy = x, Girl = n - x

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

The relative frequencies = 0.375/0.625 = 0.60