Question

It is commonly assumed that babies are equally likely to come as either a boy or a girl. This is not true. Actually, about 51.3% of all babies are boys. If a family has two children (not twins), what is the chance both children are boys

Answer 1

Answer: 0.263169

Explanation:

Since for every child there is two outcomes (either a boy or a girl), so it is a binomial distribution.

Let x = Number of boys

Given: probability that a child is a boy: p= 0.513

Binomial distribution formula :
`P(X=x)=^nC_xp^x(1-p)^(n-x)`

Now, the probability that both children are boys=
`P(X=2)=^2C_2(0.513)^2(1-0.513)^0`

`=(1)(0.513)^2(1)\\\\=0.263169`

The chance both children are boys = 0.263169