Chapter 11.8, Problem 18E

To determine

TO-DETERMINE the probability of overlapping events.

Answer to Problem 18E

The value of $\text{P}\left(\text{A or B}\right)$ is $\frac{7}{36}$ .

Explanation of Solution

Given information:

Consider the probability $\text{P}\left(\text{A}\right)=\frac{1}{6}$ , $\text{P}\left(\text{B}\right)=\frac{1}{9}$ and $\text{P}\left(\text{A and B}\right)=\frac{3}{36}$ .

Calculation:

The resultant probability $\text{P}\left(\text{A or B}\right)$ can be obtained by

  $\begin{array}{l}\text{P}\left(\text{A or B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)-\text{P}\left(\text{A and B}\right)\left[\text{Probability of overlapping events}\right]\\ \text{P}\left(\text{A or B}\right)=\frac{1}{6}+\frac{1}{9}-\frac{3}{36}\left[\text{Substitute the probabilities}\right]\\ \text{P}\left(\text{A or B}\right)=\frac{7}{36}\left[\text{Simplify}\right]\end{array}$

Hence, the value of $\text{P}\left(\text{A or B}\right)$ is $\frac{7}{36}$ .