The USA Today article referenced in Exercise 6.40 also gave information on seat belt usa...

The USA Today article referenced in Exercise 6.40 also gave information on seat belt usage by age, which is summarized in the following table:

Consider the following events: S = event that a randomly selected individual uses a seat belt regularly, A₁ = event that a randomly selected individual is in age group 18–24, and A₆ = event that a randomly selected individual is in age group 65 and older.

(Reference Exercise 6.40)

USA Today (June 6, 2000) gave information on seat belt usage by gender. The proportions in the following table are based on a survey of a large number of adult men and women in the United States.

Assume that these proportions are representative of adult Americans and that an adult American is selected at random.

a. What is the probability that the selected adult regularly uses a seat belt?

b. What is the probability that the selected adult regularly uses a seat belt given that the individual selected is male?

c. What is the probability that the selected adult does not use a seat belt regularly given that the selected individual is female?

d. What is the probability that the selected individual is female given that the selected individual does not use a seat belt regularly?

e. Are the probabilities from Parts (c) and (d) equal? Write a couple of sentences explaining why this is so.