Two standard dice are rolled, what is the probability of rolling a total of 9?

$\frac{4}{36} = \frac{1}{9}$

Explanation:

There are 36 possible rolls:

$\left(\begin{matrix}\textcolor{w h i t e}{0} & \underline{1} & \underline{2} & \underline{3} & \underline{4} & \underline{5} & \underline{6} \\ 1 | & 2 & 3 & 4 & 5 & 6 & 7 \\ 2 | & 3 & 4 & 5 & 6 & 7 & 8 \\ 3 | & 4 & 5 & 6 & 7 & 8 & 9 \\ 4 | & 5 & 6 & 7 & 8 & 9 & 10 \\ 5 | & 6 & 7 & 8 & 9 & 10 & 11 \\ 6 | & 7 & 8 & 9 & 10 & 11 & 12\end{matrix}\right)$

and of those, 4 result in a nine. Therefore, the probability of rolling a 9 is:

$\frac{4}{36} = \frac{1}{9}$

Jul 8, 2018

$\frac{1}{4}$

Explanation:

If we roll two $6$ sided dice, the number of outcomes is equal to

$6 \times 6$, or $36$. This will be our denominator.

How many ways can we get a $9$ with two dice?

We can get the following:

$6 , 3$

$5 , 4$

$4 , 5$

$3 , 6$

There are four ways of getting $9$ with two dice. This will be ur numerator. Thus, we have

$\frac{9}{36}$, which can be simplified to $\frac{1}{4}$.

Therefore, the probability of rolling a $9$ with two dice is $\frac{1}{4}$.

Hope this helps!