Problem 3: In a certain population, 80% drinks, 15% smokes, and 13% both drinks and smokes. A subject is chosen at random from this population.
Events: D = Drinks, S = Smokes, DS = Drinks and Smokes
(a) Fill in the following blanks and use these values to complete the table below.
Probabilities: P(D) = ______, P(S) = ______, P(DS) = ______
Probabilities | Smokes (S) | Not Smokes (S̅) | Total
Drinks (D) | P(DS) = | P(DS̅) = | P(D) =
Not Drink (D̅) | P(D̅S) = | P(D̅S̅) = | P(D̅) =
Total | P(S) = | P(S̅) = | 1.00
(b) What is the probability the person does not drink?
(c) What is the probability the person drinks or smokes?
(d) If the person drinks, what is the probability that he or she smokes?
(e) If the person does not smoke, what is the probability that he or she drinks?
(f) Are the events "Drinks" and "Smokes" mutually exclusive? (State "Yes" or "No" and explain.)
(g) Are the events "Drinks" and "Smokes" independent? (State "Yes" or "No" and explain.)