Suppose three competing airlines each schedule their own flight to Waco which arrives there between 2:00 and 3:00 pm according to a continuous uniform distribution. All three flights are mutually independent.

(a) If Ralph shows up at the airport at 2:00 and decides he will watch all three arrivals, what is the expected time that he observes the third and last arrival?

(b) If each airline’s flight only stays on the ground for 10 minutes, find or estimate the probability that all 3 airlines will have a plane on the ground at Waco at some point in the hour from 2:00 to 3:00.