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?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)