Question

Two dice are rolled. Write the sample space S and number of sample points n(S). Also write the events in the set form and number of sample points in the event according to the given condition.

Condition for event A: The sum of the digits on upper face is a multiple of 5.

Condition for event B: The sum of the digits on upper face is 25.

Answer 1

Two dice are rolled.

∴ The sample space

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)}

∴ n(S) = 36.

(a) Event A: The sum of the digits on the upper face is a multiple of 5.

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

∴ n(A) = 7

(b) Event B: The sum of the digits on the upper face is 25.

B = { }

Because the maximum sum of the digits on the upper face is 12.

∴ n(B) = 0