Question

You are rolling two dice at the same time. What is the probability of rolling a sum of 5 or 9?

Answer 1

`5: 1/9`
`9: 1/9`

Explanation:

First, we can take a look at all of the `36` possible outcomes of rolling two dice. Remember, the two results are independent.

Possibility of 5
We can check the table to see which results sum to `5`.

`(4,1)`
`(1,4)`
`(3,2)`
`(2,3)`

We could do this even without the table because of an understanding of the numbers that sum to `5`.

There are `4` possibilities that sum to `5` out of the total `36` possibilities. The probability is `4/36` or `1/9`.

Possibility of 9

We can apply the same principles as before to this problem.

Checking the table, we see that the following sum to `9`.

`(6,3)`
`(3,6)`
`(5,4)`
`(4,5)`

There are other combination that sum to `9`, such as `(7,2)`, but they exceed the limits of the dice.

Therefore, we again have `4` possibilities and a `1/9` probability.