13. At the intersection of two remote roads, the vehicles arriving are either cars or trucks.

Suppose that cars arrive at the intersection at a Poisson rate of λ per minute, and trucks arrive at a Poisson rate of μ per minute. Suppose that the arrivals are independent of each other. If we are given that the next vehicle arriving at this intersection is a car, find the expected value of the time until the next arrival.

Warning: Since cars and trucks arrive at this intersection independently, we might fallaciously think that, given the next arrival is a car, the expected value until the next arrival is 1/λ.