Question

Two die are rolled, A is the event that the sum of the numbers shown on the two die is 7 and B is the event that at least one of the die shows up 2. Are the two events A and B

1. Mutually exclusive

2. Exhaustive.

Answer 1

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5),(2,6), (3, 1) , (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

A = {(6, 1), (1, 6), (4, 3), (3, 4), (2, 5), (5, 2)}

B = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (1, 2), (3, 2), (4, 2), (5, 2), (6, 2)}

1. Now; A ∩ B = {(2, 5), (5, 2)} ≠ Φ

Therefore not mutually exclusive.

2. A ∪ B = {(6, 1), (1, 6), (4, 3), (3, 4), (2, 5), (5, 2), (2, 1), (2, 2), (2, 3), (2, 4), (2, 6), (1, 2), (3, 2), (4, 2), (6, 2)} ≠ S

Therefore not mutually exhaustive.