Question

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:A: the sum is greater than 8, B: 2 occurs on either dieC: the sum is at least 7 and a multiple of 3.Which pairs of these events are mutually exclusive? Select the correct answer from above options

Answer 1

Event `A : `Event that the sum of two dice is greater than `8`. `A: {(4,5),(5,4),(6,3),(3,6),(4,6),(6,4),(5,5),(6,5),(5,6),(6,6)}` Event `B : `Event that `2` occurs on either dice. `B: {(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(1,2),(3,2),(4,2),(5,2),(6,2)}` Event `C : `Event that the sum is at least `7` and a multiple of `3`. `C: {(4,5),(5,4),(6,3),(3,6),(6,6)}` Here, `A nn C != phi`, so `A` and `C` are not mutually exclusive events. `AnnB = phi,` so `A` and `B` are mutually exclusive events. `BnnC = phi,` so `B` and `C` are mutually exclusive events.