Soda drinkers in a group were classified in two ways: By gender and by soda pref

Question

Soda drinkers in a group were classified in two ways: By gender and by soda preference among three given brands. The results are shown in the following table. Suppose a member of this group is selected at random. (a) What is the probability that the person prefers Pepsi? (b) What is the probability that the person who preferred Pepsi is male? (c) What is the probability that a person who prefers Pepsi is male? (d) Are the events "member prefers Pepsi" and "member is male" mutually exclusive? Justify your answer. (e) Are the events "member prefers Pepsi" and "member is male" independent? Justify your answer.

Explanation / Answer

a) probability that person prefers pepsi =450/1000=0.45

b)probability =270/1000=0.27

c)probability =270/450=0.6

d)No as they contain 270 values in common, for mutually exclusive value in common should be 0

e) No as P(male and pepsi)=0.27

P(male)=350/1000=0.35

and P(pepsi)=450/1000=0.45

as P(male)*P(pepsi) is not equal to P(male and pepsi) they are not independent

coke pepsi shasta Total gender female 140 180 80 400 male 210 270 120 600 total 350 450 200 1000

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