Question

there are 16 boys and 24 girls in the school choir. the choir director is going to randomly select 2 choir members to sing the national anthem at next weeks pep rally. what is the probability that both of the selected singers will be boys? select the correct answer.

Explanation:

Step1: Calculate total number of choir members

Total members = 16 (boys)+24 (girls)=40

Step2: Calculate probability of first - selected being a boy

The probability that the first - selected singer is a boy is $P_1=\frac{16}{40}=\frac{2}{5}$

Step3: Calculate probability of second - selected being a boy given first is a boy

After one boy is selected, there are 15 boys left and 39 total members left. So the probability that the second - selected singer is a boy given the first one is a boy is $P_2=\frac{15}{39}=\frac{5}{13}$

Step4: Calculate probability of both being boys

Since these are dependent events, the probability that both selected singers are boys is $P = P_1\times P_2=\frac{2}{5}\times\frac{5}{13}=\frac{2}{13}$

Answer:

$\frac{2}{13}$