Vehicles approaching a crossroads must go in one of three directions-left, right or straight on. Observations by traffic engineers showed that of vehicles approaching from the north, 45% turn left, 20% turn right and 35% go straight on. Assuming that the driver of each vehicle chooses direction independently, what is the probability that of the next three vehicles approaching from the north

(a) all go straight on,

(b) all go in the same direction,

(c) two turn left and one turns right,

(d) all go in different directions,

(e) exactly two turn left? Given that three consecutive vehicles all go in the same direction, what is the probability that they all turned left? (AEB)