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 die.

C : The sum is at least 7 and a multiple of 3.

Which pairs of these events are mutually exclusive?

A pair of dice is rolled.

∴ The sample space is:

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)}

Event A: the sum of numbers on the two dice is greater than 8.

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

Event B: two occurs on either die

Two occurs on first die, the second die or both.

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

Event C: the sum is at least 7 and is divisible by 3

C = {(3,6), (4,5), (5,4), (6,3), (6,6)}

Now, = {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}

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

=

∴ A and B are mutually exclusive.

= {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)}

{(3,6), (4,5), (5,4), (6,3), (6,6)}

= {(3,6), (4,5), (5,4), (6,3), (6,6)

∴ A and C are not mutually exclusive.

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

{(3,6), (4,5), (5,4), (6,3), (6,6)}

=

∴ B and C are mutually exclusive.