A fair 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