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

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 lamda per minute, and trucks arrive at a Poisson rate of mil 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.