If you had to construct a mathematical model for events A and B, as described below, would it be appropriate to assume that A and Bare independent? Explain the reasons for your opinion.
(i) A is the event that a subscriber to a certain magazine owns a car, and B is the event that the same subscriber is listed in the telephone directory.
(ii) A is the event that a married man has blue eyes, and B is the event that his wife has blue eyes.
(iii) A is the event that a man aged 21 is more than 6 feet tall, and B is the event that the same man weighs less than 150 pounds.
(iv) A is the event that a man lives in the Northern Hemisphere, and B is the event that he lives in the Western Hemisphere.
(v) A is the event that it will rain tomorrow, and B is the event that it will rain within the next week.