# If three dice are rolled, what is the probability of getting a total of 18?

Jan 23, 2018

$\frac{1}{216}$

#### Explanation:

to obtain a total of $18$ we need all three dice to show a $6$

because they are independent events we can simply multiply the separate probabilities

$P \left(18\right) = P \left(6 \cap 6 \cap 6\right)$

$= P \left(6\right) \times P \left(6\right) \times P \left(6\right) = \frac{1}{6} \times \frac{1}{6} \times \frac{1}{5}$

$= \frac{1}{216}$