Chapter 13.4, Problem 55E

a.

To determine

To find whether the events are mutually exclusive or mutually inclusive.

Answer to Problem 55E

The event is mutually inclusive.

Explanation of Solution

Given:

The probability that the engine is flooded is $\frac{1}{2}$ and the probability that the battery is dead is $\frac{2}{5}$ and the probability that both the engine is flooded and the battery is dead is $\frac{1}{10}$ .

Calculation:

The event is mutually inclusive because the engine can be flooded and the battery is dead simultaneously.

b.

To determine

To draw a Venn diagram to represent the events.

Explanation of Solution

Given:

The probability that the engine is flooded is $\frac{1}{2}$ and the probability that the battery is dead is $\frac{2}{5}$ and the probability that both the engine is flooded and the battery is dead is $\frac{1}{10}$ .

Calculation:

The following is the Venn diagram

  

c.

To determine

To find the probability that car will not start because of flooded engine or dead battery.

Answer to Problem 55E

  $\frac{1}{5}$

Explanation of Solution

Given:

The probability that the engine is flooded is $\frac{1}{2}$ and the probability that the battery is dead is $\frac{2}{5}$ and the probability that both the engine is flooded and the battery is dead is $\frac{1}{10}$ .

Calculation:

The probability that car will not start because of flooded engine or dead battery.

  $\begin{array}{l}\frac{1}{2}+\frac{2}{5}-\frac{1}{10}\\ =\frac{1}{5}\end{array}$