Chapter 11.8, Problem 15E

To determine

TO-DETERMINE the probability of disjoint events.

Answer to Problem 15E

The value of $\text{P}\left(\text{A or B}\right)$ is $\frac{7}{10}$ .

Explanation of Solution

Given information:

Consider the probability $\text{P}\left(\text{A}\right)=\frac{13}{50}$ and $\text{P}\left(\text{B}\right)=\frac{22}{50}$ are disjoint.

Calculation:

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

  $\begin{array}{l}\text{P}\left(\text{A or B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)\left[\text{Probability of disjoint events}\right]\\ \text{P}\left(\text{A or B}\right)=\frac{13}{50}+\frac{22}{50}\left[\text{Substitute the probabilities}\right]\\ \text{P}\left(\text{A or B}\right)=\frac{35}{50}\left[\text{Add}\right]\\ \text{P}\left(\text{A or B}\right)=\frac{7}{10}\left[\text{Simplify}\right]\end{array}$

Hence, the value of $\text{P}\left(\text{A or B}\right)$ is $\frac{7}{10}$ .