Suppose traffic engineers have coordinated the timing of two traffic lights to encourage a run of green lights. In particular, the timing was designed so that with probability 0.8 a driver will find the second light to have the same color as the first. Assuming the first light is equally likely to be red or green,
(a) what is the probability P(G2) that the second light is green?
(b) what is P(W), the probability that you wait for at least one light?
(c) what is P(G1 | R2), the conditional probability of a green first light given a red second light?