If you had to construct a mathematical model for events E and F, as described in parts (a) through (e), would you assume that they were independent events? Explain your reasoning.

a. E is the event that a businesswoman has blue eyes, and F is the event that her secretary has blue eyes.

b. E is the event that a professor owns a car, and F is the event that he is listed in the telephone book.

c. E is the event that a man is under 6 feet tall, and F is the event that he weighs more than 200 pounds.

d. E is the event that a woman lives in the United States, and F is the event that she lives in the Western Hemisphere.

e. E is the event that it will rain tomorrow, and F is the event that it will rain the day after tomorrow.