38. A Morgan Stanley Consumer Research Survey sampled men and women and asked each whether they preferred to drink plain bottled water or a sports drink such as Gatorade or Propel Fitness water (The Atlanta Journal-Constitution, December 28, 2005). Suppose 200 men and 200 women participated in the study, and 280 reported they preferred plain bottled water. Of the group preferring a sports drink, 80 were men and 40 were women.

Let M  the event the consumer is a man W  the event the consumer is a woman B  the event the consumer preferred plain bottled water S  the event the consumer preferred sports drink

a. What is the probability a person in the study preferred plain bottled water?

b. What is the probability a person in the study preferred a sports drink?

c. What are the conditional probabilities P(M  S) and P(W  S) ?

d. What are the joint probabilities P(M  S) and P(W  S)?

e. Given a consumer is a man, what is the probability he will prefer a sports drink?

f. Given a consumer is a woman, what is the probability she will prefer a sports drink?

g. Is preference for a sports drink independent of whether the consumer is a man or a woman? Explain using probability information.