Question

I have two fair four-sided dice. The dice are both numbered 3, 4, 5 and 6 I am going to roll both dice and multiply the scores. What is the probability that the product is a multiple of 3?

Answer 1

3/4

Explanation:

We want to know the probability or rolling two numbers such that their product is a multiple of 3. If we have 2, 4-sided dice then the total number of outcomes is 16 because 4² = 16.

Think about what numbers result in a multiple of 3.
3, 3
3, 4
3, 5
3, 6
4, 3
4, 4
4, 5
4, 6
5, 3
5, 4
5, 5
5, 6
6, 3
6, 4
6, 5
6, 6

Of the possible outcomes above, only the ones in bold result in multiples of 3. So, the probability of rolling both dices and having their product be a multiple of 3 is 12/16, or 3/4.