Question

In a family of $3$ children, find the probability of having at least $1$ boy.

Answer 1

In a family of $3$ children, to find the probability of having at least $1$ boy, let us find the probability of no boy.

The sample space for different cases contains $2^3=8$ points. [ As there are $3$ children and the child may be boy or a girl] among which there is only one case when there are all girls that means no boy.

So probability of no boy is $\frac{1}{8}$.

So the probability of at least one boy is $1-\frac{1}{8}=\frac{7}{8}$.