The key formula on the second page is the formula needed to use to complete number 38. This is supplementary exercise to help me. Solution and explanation.
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.
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 woman? Explain using probability information.
Attachment:- Statistics 38 and key formula.zip