Question

An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. What is the probability that the sum of the dots is divisible by 3?

Answer 1

The first die can come in 6 different ways as can the second die.

This gives a total of 36 ways.

However 1-1 , 2-2, etc. can only come up once so the total ways for two die to be arranged is 30.

Now enumerate the total that are divisible by 3:

1-2 and 2-1 2 ways for a total of three

1-5 5-1 2-4 4-2 3-3 5 ways for a total of six

4-5 5-4 6-3 3-6 4 ways for a total of nine

6-6 for a total of 12

So there are 12 ways to get a total divisible by 3

This gives a probability of 12/30 = 2/5