Question

Imagine a country where only one of every 5 births is a girl. To increase their chances of having a girl, a family is willing to have many children. What is the probability that the first girl they have is the fourth baby?

Answer 1

0.1024

Explanation:

Given that in a country there is only one of every 5 births is a girl.

i.e probability of a child born being a girl = 0.20

EAch birth is independent of the other and there are only two outcomes

Hence X no of girls will be binomial.

Required probability

= Probability that the first girl they have is the fourth baby

= Probability for first three children to be boys and fourth be a girl

Since each birth is independent of other, we have

Required probability

=
`0.8^3*0.2\\=0.1024`