In a certain town, there are two competing taxicab companies, Red Cab and Blue Cab. The taxis mix with downtown traffic in a random manner. There are three times as many Red taxis as there are Blue taxis. Suppose that you stand on a downtown street corner and count the number X of Red taxis that appear before the first Blue taxi appears.

(a) Determine the formula for Pr (X = n).

(b) What is the likelihood of observing at least three Red taxis before the first Blue taxi?

(c) What is the average number of consecutive Red taxis prior to the appearance of a Blue taxi?