The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L. M.) brings his car in at time 0 and Sally Carrera (S. C) brings her car in at time t, what is the probability that S. C.'s car is ready before L. M.'s car? Assume that service times are independent and service begins upon arrival of the car. Be sure to: 1) define all random variables used. 2) explain how independence of service times plays a part in your solution. 3) show all integration steps. (b) If both cars are brought in at time 0, with work starting on S. C.'s car only when L. M.'s car has been completely serviced, what is the probability that S. C.'s car is ready before time 2?
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