Question

A die is rolled. What is the probability that the number is a factor of 6 or more than 2? Does this scenario represent mutually exclusive or mutually inclusive events?

Answer 1

Factors of 6 are : 1,2,3 and 6.

Let us find probability of getting the number that is a factor of 6.

`P(\text{ The number is a factor of 6})=(4)/(6) =(2)/(3)`

Now let us find probability of getting a number more than 2 (3,4,5,6).

`P(\text{ The number is a greater than 2})=(4)/(6) =(2)/(3)`

We can see that these two events are mutually inclusive events. We can find probability of mutually inclusive events by formula
`P(\text{X or Y})=P(X)+P(Y)-P(\text{X and Y})`.

`P(\text{ The number is a factor of 6 and greater than 2})=(2)/(6) =(1)/(3)`

Now we will find probability of getting the number is a factor of 6 or more than 2 using above formula.

`P(\text{ The number is a factor of 6 or greater than 2})=(2)/(3) +(2)/(3)-(1)/(3)`

`P(\text{ The number is a factor of 6 or greater than 2})= (4)/(3)-(1)/(3)=(3)/(3)=1`

Therefore, our probability will be 1 and this scenario represents mutually inclusive events.