Chapter 12, Problem 19CT

To determine

Solve the problem.

Answer to Problem 19CT

We cannot use the given formula.

Explanation of Solution

Given information:

Given: Use the formula $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$ to solve a problem about mutually exclusive events.

Calculation:

Here, we have:

  $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)\mathrm{............}\left(1\right)$

Now, two events are mutually exclusive if the outcomes of both the events are not common.

Now, if $AandB$ are mutually exclusive events then the probability of $P\left(AandB\right)$ is defined as:

  $P\left(AandB\right)=P\left(A\right)+P\left(B\right)\mathrm{...........}\left(2\right)$

Thus, if the two events are mutually exclusive then the overlapping of the events occur due to which $P\left(AandB\right)becomes0.$

Hence, we cannot use the formula $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$ to solve the problem.