# Determine whether events A and B are mutually exclusive. A red die and a blue die are rolled. ...

## Question:

Determine whether events A and B are mutually exclusive.

A red die and a blue die are rolled.

A: The red die comes up 5.

B: The total is 4.

## Mutually exclusive event

The mutually exclusive event are those events which cannot occur simultaneously, there is no intersection between the two events, and the events are also known as disjoint events.

Given Information

Red die and blue die are rolled.

Probability of event A red die comes up 5 is calculated as follows;

{eq}P\left( A \right) = \dfrac{1}{6} {/eq}

Probability of total of two event A and B is (4) is calculated as follows;

The number of outcomes which has sum equal to 4, is given as;

{eq}\left\{ {\left( {1,3} \right)\left( {2,2} \right)\left( {3,1} \right)} \right\} {/eq}

{eq}\begin{align*} P\left( {Sum = 4} \right) &= \dfrac{3}{{36}}\\ &= \dfrac{1}{{12}} \end{align*} {/eq}

There is no number 5 in the sample space of event B, hence there is no interaction between the two events.

Therefore, the events A and B are not mutually exclusive.