Question

A science class has 7 girls and 1 boy in the seventh grade and 3 girls and 9 boys in the eighth grade. The teacher randomly selects a seventh and an eighth-grader from the class for a competition. What is the probability that the students she selects are both girls?Write your answer as a fraction in the simplest form.

Answer 1

7/32

Explanation:

The seventh-grade class has 7 girls and 1 boy.

`P(\text{selecting a girl from seventh grade)}=(7)/(7+1)=(7)/(8)`

The eighth-grade class has 3 girls and 9 boys.

`P(\text{selecting a girl from eighth grade)}=(3)/(3+9)=(3)/(12)`

Therefore, the probability that the students she selects are both girls:

`P(\text{both are girls)}=(7)/(8)*(3)/(12)=(7)/(32)`

The probability is 7/32.