Question

If two dice are rolled simultaneously, find the probability of the following events.

Event B: The sum of the digits on the upper faces is 33.

Answer 1

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

Let B be the event that the sum of the digits on the upper faces is 33.

The sum of the digits on the upper faces can be maximum 12.

∴ Event B is an impossible event.

∴ B = { }

∴ n(B) = 0

∴ `P(B) = (n(B))/(n(S))`

= `0/36`

∴ P(B) = 0