7.34 Vehicles arriving at an intersection can turn right or left or can continue straight ahead. In a study of traffic patterns at this intersection over a long period of time, engineers have noted that 40% of the vehicles turn left, 25% turn right, and the remainder continue straight ahead.

a For the next five cars entering the intersection, find the probability that one turns left, one turns right, and three continue straight ahead.

b For the next five cars entering the intersection, find the probability that at least one turns right.

c If 100 cars enter the intersection in a day, find the expected value and variance of the number turning left. What assumptions are necessary for your answer to be valid?