A standard die is rolled six times. What is the probability that the product of all six rolls is divisible by 3? Express your answer as a common fraction.
+128407 It may be easier to figure out the number of products that are not divisible by 3
For this to happen we cannot have any roll = 3 or 6
So....... we can roll either a 1 or a 2 or a 4 or a 5 on any roll (since none of these are divisible by 3 )
The number of possible rolls in this case = 4^6 (we can choose any of the 4 numbers above on each roll)
And the number of possible rolls in all cases = 6^6
So....the probability that any product is divisible by 3 is
1 - 4^6 / 6^6 =
1 - (2/3)^6 =
1 - 64/729 =
665 / 729
