Question

A small class has 9 students, 6 of whom are girls and 3 of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the teacher will choose two boys? Write your answer as a fraction in simplest form.

Answer 1

To find the probability of the teacher choosing two boys out of a class of 9 students (6 girls and 3 boys), we need to calculate the probability of selecting one boy followed by another boy.

The probability of selecting the first boy is 3/9 (since there are 3 boys out of 9 students). After selecting the first boy, there will be 2 boys left out of the remaining 8 students.

Therefore, the probability of selecting the second boy, given that the first boy was chosen, is 2/8.

To find the probability of both events occurring (selecting two boys in a row), we multiply the probabilities:

(3/9) * (2/8) = 6/72 = 1/12

So, the probability that the teacher will choose two boys is 1/12.