Question

If you roll a pair of dice, what is the probability of rolling either a single 5 or a sum that is an even number?

Answer 1

`2/3`

Explanation:

Note that total number of possible cases are `6^2= 36`

Getting a single `5` ( Say event `A` ) means situation like as `(1,5),(2,5),(3,5),(4,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6)` i.e. `10` cases and we have `18` cases when sum is an even number ( Say event `B` ) . But these two events are not mutually exclusive. Here `(1,5),(3,5),(5,1),(5,3)` i.e. `4` cases where we get a single `5` as well as sum is a even number ( Say event `A nn B` ) .

So we have number of favorable cases to our event `= n(A)+n(B)-n(A nn B) = 10+18-4=24`

So required probability `= 24/36=2/3`