A fair die is rolled five times What is the probability that

A fair die is rolled five times. What is the probability that none of rolls produces a \"3\"?

Solution

A roll can produce 1,2,3,4,5,6

So, not 3 would mean, it can be any of 1,2,4,5 or 6

So, on each roll, we have 5 favorable out of a total of 6 outcomes

P(none 3) = (5/6)(5/6)(5/6)(5/6)(5/6)

P(none 3) = 5^5 / 6^5 ---> exact form of the answer

= 0.401878 approximated to 6 decimal places