Two dice are rolled. What is the probability that the product of the numbers obtained on the two dice is divisible by 6?
In the following table, we mark with $\times$ the products that are divisible by 6.

| $\times$ | 1 | 2 | 3 | 4 | 5 | 6 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 1 |  |  |  |  |  | $\times$ |
| 2 |  |  | $\times$ |  |  | $\times$ |
| 3 |  | $\times$ |  | $\times$ |  | $\times$ |
| 4 |  |  | $\times$ |  |  | $\times$ |
| 5 |  |  |  |  |  | $\times$ |
| 6 | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ | $\times$ |

Thus, we have 15 favorable cases out of 36 possibilities. Therefore, the probability that the product is divisible by 6 is $15 / 36=5 / 12=41.7\%$.