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?

1 Answer
MeneerNask
Jul 6, 2018

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%

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