Question

A family has 8 girls and 4 boys. A total of 2 children must speak on behalf of the family at a local benefit. What is the probability that at least one boy will be chosen?

Answer 1

Let's look at the probability that no boy is chosen.

Explanation:

First selection:
`P(girl)=8/12=2/3`

Second selection:
`P(girl)=7/11`

Combined probability of first AND second being a girl
(Remember AND means MULTIPLY):

`P(2 girls)=P(0boys)=2/3xx7/11=14/33`

The probability of at least one boy is then the complement of this, or in other words:

`P(1or 2 boys)=1-P(2 girls)=1-14/33=19/33~~58%`