Question

Find the probability that when a couple has ​children, at least one of them is a . ​(Assume that boys and girls are equally​ likely.)

Answer 1

`P(At\ least\ one\ girl) = 0.875`

Explanation:

Given

`n = 3`

`B \to boys`

`G \to girls`

`P(G) = P(B) = 0.5` --- equal probability

See comment for complete question

Required:

`P(At\ least\ one\ girl)`

To do this, we make use of complement rule:

`P(At\ least\ one\ girl) = 1 - P(No\ girl)`

The event that there is no girl out of the 3 children is: B B B

And the probability is:

`P(No\ Girl) = P(B) * P(B) * P(B)`

`P(No\ Girl) = 0.5*0.5*0.5`

`P(No\ Girl) = 0.125`

So:

`P(At\ least\ one\ girl) = 1 - P(No\ girl)`

`P(At\ least\ one\ girl) = 1 - 0.125`

`P(At\ least\ one\ girl) = 0.875`