# If you roll a fair die three times, what is the probability that none of your rolls is a number divisible by 3?

Nov 3, 2015

$\frac{8}{27}$

#### Explanation:

When a fair die is thrown, the probability of getting each of the digit 1,2,3,4,5 and 6 is $\frac{1}{6}$.

Of these, digits divisible by 3 are 3 and 6.
Hence when you roll a fair die once, probability of getting a number divisible by 3 is $\frac{2}{6}$ or $\frac{1}{3}$.
Probability of getting a number not divisible by 3 in one roll is $\frac{2}{3}$
Since the die is rolled 3 times, tje required probability is ${\left(\frac{2}{3}\right)}^{3}$ or $\frac{8}{27}$.