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

##### 1 Answer

Nov 3, 2015

#### Explanation:

When a fair die is thrown, the probability of getting each of the digit 1,2,3,4,5 and 6 is

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#2/6# or#1/3# .

Probability of getting a number not divisible by 3 in one roll is#2/3#

Since the die is rolled 3 times, tje required probability is#(2/3)^3# or#8/27# .