Afair die is rolled repeatedly. use precise notation of probabilities of events and random variables for the solutions to the questions below.

(a) write down a precise sum expression for the probability that the first five rolls give a 3 at most two times.

(b) calculate the probability that the first 3 does not appear before the fifth roll.

(c) calculate the probability that the first 3 appears before the twentieth roll but not before the fifth roll