Assume that an old used car fails to start 10% of the time. The other 90% of the time it drives for a time period which is uniformly distributed in the interval 20 to 30 minutes. In this interval all subintervals of time of equal width between 20 to 30 minutes are equally likely.
(a) What is the probability that the car drives for at least 10 minutes given that it starts?
(b) What is the probability that the car drives for at least 10 minutes?