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