# 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?

Jul 6, 2018

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

#### Explanation:

First selection:
$P \left(g i r l\right) = \frac{8}{12} = \frac{2}{3}$

Second selection:
$P \left(g i r l\right) = \frac{7}{11}$

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

$P \left(2 g i r l s\right) = P \left(0 b o y s\right) = \frac{2}{3} \times \frac{7}{11} = \frac{14}{33}$

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%