In a second grade class containing 13 girls and 9 boys, 2 students are selected at random to give out the math papers. What is the probability that the second student chosen is a boy, given that the first one was a girl?

Question

Quizplus · Accepted Answer

We need to use conditional probability to solve this problem.

Let's denote the event that the first student chosen is a girl as G and the event that the second student chosen is a boy as B.

We want to find the probability of B given that G has already occurred: P(B|G)

Using the formula for conditional probability, we have:

P(B|G) = P(G and B) / P(G)

The probability that the first student chosen is a girl is given by:

P(G) = number of girls / total number of students = 13/22

Since one girl has already been chosen, there are now 12 girls and 9 boys left. So the probability that the second student chosen is a boy, given that the first one was a girl, is:

P(G and B) = number of outcomes where the first student is a girl and the second is a boy / total number of outcomes

The number of outcomes where the first student is a girl and the second is a boy is 13*9 = 117, since there are 13 ways to choose a girl for the first student and 9 ways to choose a boy for the second student. The total number of outcomes is 22*21 = 462, since there are 22 students and 21 ways to choose the second student after one has already been chosen.

So we have:

P(B|G) = P(G and B) / P(G) = 117/462 / 13/22 = 22/77 = 0.2857

This corresponds to choice C, 11eaa984_72bb_d1b5_97c0_7b409bd490a3_TB1705_11.

In a Second Grade Class Containing 13 Girls and 9