Answer to Question #299107 in Statistics and Probability for Lester San Juan

Question

Mrs. Balao is randomly choosing 3 students for a team who will compete in a math quiz bee, and there are 5 girls and 8 boys to choose from. What is the probability of having a team made up 2 girls and a boy?

Answer 1

Number of boys is 8

Number of girls is 5

Total number of students is 8+5=13

There are $\binom{5}{2}=10$ ways to choose 2 girls from 5 girls

There are $\binom{8}{1}=8$ ways to choose 1 boy from 8 boys

There are $\binom{13}{3}=286$ ways to select 3 students from 8 boys and 5 girls.

The probability of having a team made up 2 girls and a boy is ${10\times 8\over286}=0.2797$