Answer: 11/36
n(S) = \(6 \times 6 = 36\).
The product is non-zero only when both numbers are from 1 to 5: \(5 \times 5 = 25\) outcomes.
So the product is zero in \(36 - 25 = 11\) outcomes: (0,0), (0,1), ..., (0,5), (1,0), (2,0), (3,0), (4,0), (5,0).
\[ P = \frac{11}{36} \]