A man owns 2 cars. One is old and unreliable. It fails to turn on 35% of the time when he tries to use it. The other car is newer and much more reliable. It fails to turn on just 1% of the time he tries to use it.
a. If he chooses a car randomly to drive to work, what is the prior probability that the old, unreliable one would be chosen?
b. If he chooses a car randomly to drive to work, what is the prior probability that the randomly chosen car will fail to start?
c. He attempts to turn on the car he randomly selected and it turns on without any problem. Given this additional info, what is the revised probability that the selected car is the old unreliable one?