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?

Answer 1

probability of picking a girl in 4th grade class = 11/21
probability of picking a girls in 3rd grade class = 12/25

11/21 * 12/25 = 44/175 <==

Answer 2

Answer: Our required probability is
`(44)/(175)`

Explanation:

Since we have given that

In third grade class:

Number of girls = 12

Number of boys = 13

In fourth grade class

Number of girls = 11

Number of boys = 12

According to question, First caption made a selection from the fourth grade class and the other caption made a selection from the third grade class.

We need to find the probability that the first caption will pick two girls before picking any boys.

So, Probability that the first caption will pick two girls before picking any boys is given by

`P(\text{choosing girl from fourth grade})* P(\text{choosing girl from third grade})\\\\=(11)/(21)* (12)/(25)\\\\=(44)/(175)`

Hence, our required probability is
`(44)/(175)`