Question

Using Law of Total Probability

a) Two consecutive traffic lights have been synchronized to make a run of green lights more likely. In particular, if a driver finds the first light to be red, the second light will be green with probability 0.9, and if the first light is green the second will be green with probability 0.7. If the probability of finding the first light green is 0.6, find the probability that a driver will find the second traffic light red.

b)  Two consecutive traffic lights have been synchronized to make a run of green lights more likely. In particular, if a driver finds the first light to be red, the second light will be green with probability 0.9, and if the first light is green the second will be green with probability 0.7. If the probability of finding the first light green is 0.6, find the probability that a passing car encountered a red light first given that it encountered a green second light.

Answer 1

Let G1 and R1 denote the event that the first traffic light will be green and red respectively