Problem 3. Traffic on Highway 35W in Minneapolis, MN follows a Poisson process with rate 10 vehicles per minute. 10% of the vehicles are trucks, the other 90% are cars. (a) What is the probability at least 30 trucks passe in a hour? (b) Given that 100 trucks have passed by in an hour, what is the expected number of vehicles that have passed by? (c) Given that 500 vehicles have passed by in a hour, what is the probability there were exactly 50 trucks and 450 cars? (d) Given that 200 cars have passed by between 2 and 4pm and 100 trucks have passed by between 4 and 6pm, what is the probability there were 300 cars passed by Minneapolis between 3 and 5pm