Harold and Maude plan to take a cruise together, but they live in separate cities. The cruise departs from Miami, and they each book a flight to arrive in Miami an hour before they need to be on the ship. Their travel planner explains that Harold's flight has an 80% chance of making it on time for him to get to the ship and that Maude's flight has a 90% chance of making it on time.
a. How do you think the travel planner determined these probabilities?
b. Assuming that the probabilities quoted are long-run relative frequencies, do you think whether Harold's plane is on time is independent of whether Maude's plane is on time on the particular day they travel? Explain. (Hint: Consider reasons why planes are delayed.)
c. Whether realistic or not, assuming that the probabilities are independent, what is the probability that Harold and Maude will both arrive on time?
d. What is the probability that one of the two will be cruising alone?