10. In rolling 3 dice, are the events A: Sum divisible by 3 and B: Sum divisible by 5 mutually exclusive?

Answer: No, the events A and B are not mutually exclusive.

Step-by-step explanation:

We say any two events P and Q are mutually exclusive, if they are disjoint set such that their intersection is empty.

Given : In rolling 3 dice, we have two events

Event A: Sum divisible by 3

Event B: Sum divisible by 5

But the sum of all 3 dices can 15 and 15 is divisible by 3 and 5.

The intersection of events A and B have = { (5,5,5), (3,6,6), (6,3,6), (6,6,3), (5,4,6), (6,4,5), (4,6,5), (4,5,6), (6,5,4), (5,6,4) }

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