Question

Using the binomial distribution formula, find the possibility that a family that has 13 children has 10 girls.

Answer 1

A family has 13 children.

We have to find the probability that out of them, 10 are girls.

Now, we assume that a randomly chosen child is a boy, or a girl, with equal probability; ie. probability that a randomly chosen child is a boy, with probability 0.5, and the probability that a randomly chosen child is a girl, with probability 0.5.

So, if X be the number of children, out of the 13 in the family, who are girls, then,

X follows binomial with parameters n=13, and p=0.5.

So, the probability mass function of X is given by

Where, i can take integer values from 0 to 13.

Now, we have to find the probability that 10 are girls.

So,

So, the probability that a family, that has 13 children, has 10 girls, is 0.0349.