When two dice are tossed, what is the probability of the product of the numbers being 12?

A die has 6 faces marked with the numbers 1, 2, 3, 4, 5 and 6. When a fair die is rolled there is an equal probability of any of the 6 numbers showing up.

If two dice are rolled, the product of the numbers that turn up is 12 in the following cases: (2,6), (6,2), (3,4), (4,3). As each of the die can show any of the 6 numbers, there are 6*6 = 36 different possibilities. (The product in many of these is the same, but that does not make a difference in estimating the required probability.)

Of the 36 different options, 4 of them give numbers that have 12 as their product.

This gives the required probability as 4/36 = 1/9.

When 2 fair die are rolled there is a probability of 1/9 that the product of the numbers that turn up will be 12.