Chapter 11.3, Problem 8LC

Solution

To identify: The two events that are mutually exclusive.

In both these case none of the pair is common. This implies that, $P\left(CandD\right)=0$ these are mutually exclusive events.

Explanation:

Objective is to describe two events that are mutually exclusive.

For instance:

The two events that are mutually exclusive are:

Consider the experiment, rolling two dice

Event 1: The number on both dice is equal.

Event 2: The sum of numbers on two dice is odd.

Both these events are mutually exclusive.

Two fair cubes are rolled, so, the total possible cases are $6^2=36.$ The numbers are equal, the sum is odd.

Since mutually exclusive are those that cannot happen at the same time.

If C and D are mutually exclusive events, then

  $P\left(CandD\right)=0$

First event C is that numbers are equal

So. $C=\left\{\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right),\left(5,5\right),\left(6,6\right)\right\}$

That means there are 6 favorable cases.

Therefore, $P\left(C\right)=\frac{6}{36}$

Second event D is sum is odd.

So, it can be any number from $3,4,7,9\text{and}11$

There are 19 favorable cases.

Therefore, $P\left(D\right)=\frac{19}{36}$

In both these case none of the pair is common. This implies that, $P\left(CandD\right)=0$

So, these are mutually exclusive events.