Problem #38 review question need help
38. A Morgan Stanley Consumer Research Survey sampled men and women and asked each whether the 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.
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 woman? Explain using probability information.
Please answer A through G with solution and explanation.
The solution provides step by step method for the calculation of probabilities and conditional probabilities. Formula for the calculation and Interpretations of the results are also included.