Chapter 13.4, Problem 29E

To determine

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

Answer to Problem 29E

Mutually exclusive, $\frac{1}{4}$

Explanation of Solution

Given:

The probability of showing sum of $6$ or a sum of $9$ .

Calculation:

Let $A$ be the event of showing sum of $6$

Let $B$ be the event of showing sum of $9$ .

Sample space $=36$

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

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

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

Therefore probability of event $A$ is $P(A)=\frac{5}{36}$

And probability of event $B$ is $P(B)=\frac{4}{36}$

The event is exclusive because there can’t be two number that have a sum of 6 and 9 in the same time.

Hence,

  $\begin{array}{l}P(\text{A or B})=P(A)+P(B)\\ P(\text{A Or B})=\frac{5}{36}+\frac{4}{36}=\frac{9}{36}=\frac{1}{4}\end{array}$