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

Sample space of 7th grade (5 boys + 5 girls)

sample space of 8th grade (5 boys + 3 girls)


P(boy 7th grade) = 5/10 =1/2
P(boy 8th grade) = 5/8
Hence the probability of selecting a boy from 7th AND a boy from 8th is:

(1/2)x(5/8) ==> 5/16 ( It's a conditional probability)

Answer 2

So the ratios are 5:5 and 3:5 so the fractions are 5/10 (1/2) for 7th grade and 5/8 for 8th grade