Vehicles pass a point on a road according to a Poisson process with rate 1 per minute. Suppose that 25% of the vehicles are trucks and 75% of the vehicles are cars. (a) What is the probability that at least three trucks pass in a 10-minute interval? (b) Given that two trucks have passed in a 10-minute interval, what is the conditional expected number of vehicles to have passed during this time interval? (c) If 15 vehicles have passed in a 10-minute interval what is the conditional probability that 14 of them are cars?