Question

Which of the following pairs of events are mutually exclusive? Justify your response.

1. {The next customer entering a retail store is older than 30 years.}, {The next customer entering the same retail store is younger than 20 years.}
2. {The next customer entering a retail store is younger than 20 years.}, {The next customer entering the same retail store will spend more than \(900 in purchases.}
3. {The next customer entering the retail store will be older than 70 years and spend more than \)900 in purchases.}, {The next customer entering the same retail store will try to steal an item.}

Short answer

1. Both events are not mutually exclusive.
2. Both events are mutually exclusive.
3. Both events are mutually exclusive.

Step-by-step solution

Important definition

The two events are called mutually exclusive if $\mathbf{P}\mathbf{(}\mathbf{A}\cap \mathbf{B}\mathbf{)}\mathbf{=}\mathbf{0}$.

Solution for part (a)

It is possible that the data scheduled above will actually occur and is not mutually exclusive events.

Find the result for part (b)

It is impossible for all of the occurrences to happen immediately and these are mutually exclusive events.

Determine the result for part (c)

It is impossible for all of the occurrences to happen immediately and these are mutually exclusive events.