A student driving to university must pass through two sets of traffic lights. The first set of lights is green 50% of the time, yellow 10% of the time, and red 40% of the time. The second set of lights is green 60% of the time, yellow 10% of the time, and red 30% of the time. It is also known that the lights function independently. (a) The outcome of interest is the colour of each of the two lights when the student ar- rives at the intersections. List the complete sample space of outcomes, and calculate the probability of each. (b) What is the probability that both sets of lights are the same colour when the student arrives at the respective intersections? (c) What is the probability that the first light is green or the second light is red? (d) Let X be the number of red lights encountered by the student on her way to university. Find the probability distribution of X