Question

A science class has 5 girls and 5 boys in the seventh grade and 3 girls and 5 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys? Write your answer as a fraction in simplest form.

Answer 1

We have a total of 10 boys & 8 Girls, then the sample space consist of 18 elements.

P(selecting 1 boy) = (total number of boys/by 18) = P(boy)=10/18=5/9

Answer 2

Probability would be
`(5)/(16)` to select both boys.

Explanation:

To find the probability of picking two boys, we need to first know how many different ways she can pick the 7th and 8th grader.

There are 10 (5 girls and 5 boys) 7th-graders and 8 (3 girls and 5 boys) 8th-graders. So the total number of ways she can pick is:

10 × 8 = 80

To select two boys, there are 5 boys in the 7th-grade class and 5 in the 8th-grade class, so there are:

5 × 5 = 25 ways

Which gives us the probability of:

`(25)/(80)` =
`(5)/(16)`

Probability would be
`(5)/(16)` to select both boys.