Question

The time it takes for you to get to Sacramento airport is uniformly distributed between 40 minutes to 70 minutes. If you reach before 50 minutes, then you park in the economy parking lot. Otherwise you park in the garage. There are 3 stops between these parking areas and the departure terminal. If you park in the economy lot, then the time it takes between any two stops is exponentially distributed with average time equal to 20 minutes. If you park your vehicle in the garage, the time it takes between any two stops is exponentially distributed with average time equal to 10 minutes. Find the probabilities of the following scenarios while identifying the distributions used and showing complete integration work.

1. What is the probability that you reach the counter within 30 minutes after parking the vehicle?

2. Your buddy follows the same scenario as above and is lucky to park near the stop closest to the departure terminal. Your buddy tells you that it took them more than 15 minutes ride to the departure station. What is the probability that they parked in the garage?

Answer 1