Question

A third-grade class has 12 girls and 13 boys. A fourth-grade class has 10 boys and 11 girls. When picking teams for PE, one captain will make a selection from the fourth-grade class, then the other captain will make a selection from the fourth-grade class. After that, the first captain will make a selection from the third-grade class, and the second captain will do likewise. Assuming everyone has an equally likely chance of being selected, what is the probability that the first captain will pick two girls before picking any boys?

A. 44/175
B. 117/143
C. 120/143
D. 133/143

Answer 1

Let's start with 4th grade.

Total student in 4th grade is 21.
The number of ways to pick 1 girl out of 21 students is 21C1=?
21!/20!1!=21 --total outcome
The number of ways to pick 1 girl out of 11 girls in the class 11C1=?
11!/10!1!=11 --relevant outcome
Number of relevant outcome/number of total outcome=11/21 ---Probability of the first captain picking 1 girl from 4th grade.

Try the same way with 3rd grade.
Then, multiply the answer to find the probability that the first captain pick 2 girls out of 3rd grade and 4th grade.

Good Luck!

Answer 2

@haruchan
I'm not exactly sure about how you went about solving the problem, but based off your answer for the fourth grade class, it would seem that the probability of choosing a girl from the third grade class would be 12/25 , correct?
By multiplying the two, you receive 44/175.

Answer 3

Yes. that's what I got, too.

Probability of an event happening
=Number of ways it can happen/Total number of outcome

So,
There are 21 students in 4th grade: 11 girls and 10 boys.
Number of ways it can happen: 11 (There are 11 girls.)
Total number of outcome: 21 (There are 21 students in 4th grade.)

Probability of picking a girl in 4th grade is 11/21.

I hope this will help a little.