Question: Ilan and Justin are competing in a math competition. They work independently and each has the same two problems to solve. The two problems take an exponentially distributed amount of time with mean 20 and 30 minutes respectively (or rates 3 and 2 if written in terms of hours).
a) What is the probability Ilan finishes both problems before Justin has completed the first one.
b) What is the expected time until both are done?