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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.

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Sample space, 

S = {(0, 0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), (2,2), (3.0), (3,1), (3,2), (4.0), (4,1), (4,2), (5.0), (5,1), (5,2) }

∴ 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) = \(\frac{n(A)}{n(S)}\)

∴ P(A) = 11/36

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

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