(Harder problem) Two students in your engineering statistics class decide to test their knowledge of probability, which has very recently been covered in class. They each use MINITAB or other statistical software to generate a number that has a continuous uniform distribution over a specified interval. The first student uses the interval 0–3 and the second student uses the interval 0–1. Before the random numbers are obtained, the students compute the probability that the first student’s number will be at least twice the second student’s number.

(a) What is that probability?

(b) What is the probability after the random numbers have been obtained? Explain.

(c) What is the probability that the maximum of the two numbers is at most 1/2?

(d) What is the probability that the minimum of the two numbers is at least 1/4?