Question

There are 9 students in a class: 5 boys and 4 girls.

If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?

Answer 1

5/126

Explanation:

Let's go through this scenario step-by-step. At the beginning, we have a 5/9 possibility of picking a boy - 5 boys out of 9 students. If we pick 1 boy, we now have 4 boys out of 8 students we could potentially pick, giving us a 4/8 or 1/2 chance of picking a second boy after the 1st. For the third boy, we have 3 out of 7 remaining students, giving us a 3/7 chance of picking a third after the first two, and for the fourth boy, we 2 possibilities out of 6, giving us a 2/6 or 1/3 chance of picking the 4 boys.

To find the total probability, we can multiply all of these individual ones together:

`(5)/(9) \cdot(1)/(2) \cdot(3)/(7) \cdot(1)/(3)\\\\=(5)/(9) \cdot(1)/(2) \cdot(1)/(7)\\\\=(5)/(126)`