155k views
5 votes
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?

User Intelekt
by
8.6k points

1 Answer

3 votes

Answer:

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)

User Marinela
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories