Question

What is the probability of getting either a sum of 8 or at least one 4 in the roll of a pair of dice?

Answer 1

The probability of either of the incidents happening is `5/12`.

Explanation:

Here we consider two events: A - (finding a sum of `8`) & B (getting at least one `4`)

A : Probability of A is `5/36` because there are `7` such events out of `6xx6=36` events viz. `(2,6),(3,5),(4,4),(6,2),(5,3)`

B Probability of B is `11/36` because there are `11` such events out of `36` events viz.

`(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),(4,2),(4,3),(4,5),(4,6)`.

Now it is observed that the two incidents are not mutually exclusive as the incident resulting in `(4,4)` is occurs in both.

Now, the probability of either of the incidents happening is

`P(AUB)=P(A)+P(B)-P(AnnB)`

i.e. `=5/36 +11/36 -1/36=15/36=5/12`