A student must pass through two sets of traffic lights on his way to university each day.The first light is green35% of the time, yellow8% of the time and red57% of the time.The second light is green44% of the time, yellow11% of the time and red45%of the time.Suppose that it is known that the two sets of lights operate independently.

(a) On any given trip to university, what is the probability that both lights will be the same colour when the student arrives at the intersections?

(b) What is the probability that the first light will be green or that the second light will be red?

(c) LetXbe the number of times the student stops at a light on his way to school. (He will only stop if the light is red, and not if it is yellow.)Find the probability distribution ofX.