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

Total number of outcomes = 6²
= 36
Number of favourable outcomes (product of digits on the upper face is zero) = (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (2, 0), (3, 0), (4, 0) and (5, 0)
= 11
Therefore, required probability = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}$
$=\frac{11}{36}$
​Hence, the probability that the product of digits on the upper face is zero is $\frac{3}{10}$.