Chapter 13.4, Problem 25E

To determine

To find whether the pair of events is mutually exclusive or mutually inclusive and find the probability.

Answer to Problem 25E

Mutually inclusive, $\frac{11}{36}$

Explanation of Solution

Given:

The probability of tossing two number cubes and either one shows $4$ .

Calculation:

Let $A$ be the event of showing $4$ on first cube.

Let $B$ be the event of showing $4$ on second cube.

Sample space $=36$

Sample space for Event A $=(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)$

Now, sample space for event B $=(1,4),(2,4),(3,4),(4,4),(5,4),(6,4)$

The events are mutually inclusive as $(4,4)$ appears on both.

Therefore probability of event $A$ is $P(A)=\frac{6}{36}$

And probability of event $B$ is $P(B)=\frac{6}{36}$

Hence,

  $\begin{array}{l}P(\text{A or B})=P(A)+P(B)-P(A\text{ and }B\text{)}\\ P(\text{A Or B})=\frac{6}{36}+\frac{6}{36}-\frac{1}{36}=\frac{11}{36}\end{array}$