Factors of 6 are : 1,2,3 and 6.
Let us find probability of getting the number that is a factor of 6.
[tex]P(\text{ The number is a factor of 6})=\frac{4}{6} =\frac{2}{3}[/tex]
Now let us find probability of getting a number more than 2 (3,4,5,6).
[tex]P(\text{ The number is a greater than 2})=\frac{4}{6} =\frac{2}{3}[/tex]
We can see that these two events are mutually inclusive events. We can find probability of mutually inclusive events by formula [tex]P(\text{X or Y})=P(X)+P(Y)-P(\text{X and Y})[/tex].
[tex]P(\text{ The number is a factor of 6 and greater than 2})=\frac{2}{6} =\frac{1}{3}[/tex]
Now we will find probability of getting the number is a factor of 6 or more than 2 using above formula.
[tex]P(\text{ The number is a factor of 6 or greater than 2})=\frac{2}{3} +\frac{2}{3}-\frac{1}{3}[/tex]
[tex]P(\text{ The number is a factor of 6 or greater than 2})= \frac{4}{3}-\frac{1}{3}=\frac{3}{3}=1[/tex]
Therefore, our probability will be 1 and this scenario represents mutually inclusive events.
