Question

The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.

Answer 1

Sample space,

S =	{(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5),
	(1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5),
	(2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5),
	(3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5),
	(4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5),
	(5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)}

∴ n(S) = 36

Let A be the event that the product of digits on the upper face is zero.

∴ A = {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0)}

∴ n(A) = 11

∴ `P(A) = (n(A))/(n(S))`

∴ `P(A) = 11/36`

∴ The probability that the product of the digits on the upper face is zero is `11/36`.