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

May 23, 2018

$5 : \frac{1}{9}$
$9 : \frac{1}{9}$

#### 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 $5$.

$\left(4 , 1\right)$
$\left(1 , 4\right)$
$\left(3 , 2\right)$
$\left(2 , 3\right)$

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 $\frac{4}{36}$ or $\frac{1}{9}$.

Possibility of 9

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

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

$\left(6 , 3\right)$
$\left(3 , 6\right)$
$\left(5 , 4\right)$
$\left(4 , 5\right)$

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

Therefore, we again have $4$ possibilities and a $\frac{1}{9}$ probability.