There are 3 first grade children, 5 second grade children, and 6 third grade children in a room. When choosing two children, what is the conditional probability of choosing a second grade child, given that either a first or a third grade child was chosen first?

Question

Quizplus · Accepted Answer

First, let us calculate the probability of choosing a first or third grade child first: it is 9/14 (3+6 out of 3+5+6).

If we choose a first or third grade child first, we are left with 11 children (5 second graders and 6 first/third graders).

The probability of choosing a second grader out of those 11 is 5/11.

Therefore, the conditional probability of choosing a second grade child given that either a first or third grade child was chosen first is:

(Probability of choosing a second grader after choosing a first or third grader) / (Probability of choosing a first or third grader first)

= (5/11) / (9/14)

= 10/27

This matches the answer in choice B.

There Are 3 First Grade Children, 5 Second Grade Children