Let A be exponential random variable that represents the number of thousands of miles that a used auto can be

driven, \(X \sim exp(\frac{1}{20})\)

So what we want to calculate is probability that the car will cross 30 thousand miles if we have that it has already crossed 10 thousand miles:

\(P(X<30|X>10)=P(X>20+10|X>10)=P(X>20)=e^{-\frac{1}{20}\cdot 20}=0.368\)

Now let X be uniformly distriduted, \(X \sim U(0,40)\). Now we have conditional probability:

\(P(X>30|X>10)=\frac{P(X>30)}{P(X>10)}=\frac{1-P(X \le 30)}{1-P(X \le 10)}=\frac{1-30/40}{1-10/40}=\frac{1}{3}\)