Chapter 13, Problem 4E

To determine

To find the probability that a randomly selected student is a junior and a volleyball player.

Answer to Problem 4E

  $\frac{5}{9}$ .

Explanation of Solution

Given:

The following shows the information table

Calculation:

Let A be the event representing the selection of a junior and B the event representing the activity for a field day.

The probability of event A is presented by

  $P(A)=\frac{8}{27}$

Where 17 represents the total number of juniors and 27 the total number of students

The probability of event B is presented by

  $P(B)=\frac{9}{27}$

Where 9 represent the total number of students assigned to a field day and 27 the total number of students

Also, notice that there 2 students that are juniors and have been assigned to field day

  $P(A\text{ and B})=\frac{2}{27}$

Then, use the formula for not mutually exclusive events

  $\begin{array}{l}P(A\text{ or B})=\frac{8}{27}+\frac{9}{27}-\frac{2}{27}\\ =\frac{15}{27}=\frac{5}{9}\end{array}$

The probability that a randomly selected student is a junior and a volleyball player is $\frac{5}{9}$ .