Chapter 11.8, Problem 12E

To determine

To determine the probability $\text{P}\left(\text{A or B}\right)$ of disjoint events.

Answer to Problem 12E

The probability of disjoint events A and B are $\text{P}\left(\text{A or B}\right)=\frac{21}{25}$ .

Explanation of Solution

Given information:

The following probability is given:

  $\text{P}\left(\text{A}\right)=\frac{4}{25},\text{P}\left(\text{B}\right)=\frac{17}{25}$

Formula used:

The probability of disjoint events is calculated by using the following formula:

  $\text{P}\left(\text{A or B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)$

Calculation:

The probability of disjoint events can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{A or B}\right)=\text{P}\left(\text{A}\right)+\text{P}\left(\text{B}\right)\left[\text{Probability of disjoint events}\right]\\ \text{P}\left(\text{A or B}\right)=\frac{4}{25}+\frac{17}{25}\left[\text{Substitute}\right]\\ \text{P}\left(\text{A or B}\right)=\frac{21}{25}\left[\text{Add}\right]\end{array}$

Hence, the probability of disjoint events A and B are $\text{P}\left(\text{A or B}\right)=\frac{21}{25}$ .