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A selection of soft-drink users is asked to taste the two disguised soft drinks and indicate which they prefer. The accompanying data contains the results of a simulated challenge on a college campus.
Age Preference Age Preference Age Preference Age Preference Age Preference Age Preference
17 Brand B 21 Brand A 21 Brand B 19 Brand A 21 Brand A 18 Brand B
19 Brand A 16 Brand A 18 Brand B 23 Brand B 19 Brand B 22 Brand B
21 Brand A 20 Brand A 21 Brand A 24 Brand A 19 Brand A 22 Brand B
19 Brand B 19 Brand A 16 Brand A 19 Brand A 20 Brand B 21 Brand A
18 Brand A 19 Brand A 19 Brand B 21 Brand B 18 Brand A
24 Brand B 21 Brand B 23 Brand A 20 Brand A 20 Brand B
22 Brand A 18 Brand A 17 Brand B 22 Brand B 20 Brand A
20 Brand A 20 Brand A 19 Brand B 21 Brand B 17 Brand B
22 Brand B 22 Brand A 24 Brand A 22 Brand B 21 Brand B
19 Brand B 19 Brand A 20 Brand A 21 Brand B 20 Brand A
16 Brand A 24 Brand A 24 Brand A 22 Brand B 17 Brand B
16 Brand A 21 Brand B 16 Brand B 18 Brand B 21 Brand A
21 Brand B 22 Brand A 18 Brand B 22 Brand B 16 Brand A
22 Brand B 21 Brand B 22 Brand B 20 Brand B 16 Brand A
22 Brand B 20 Brand A 19 Brand B 19 Brand B 23 Brand B
19 Brand B 19 Brand A 22 Brand A 19 Brand B 20 Brand B
24 Brand B 22 Brand A 23 Brand B 23 Brand B 21 Brand A
17 Brand A 21 Brand A 16 Brand B 22 Brand A 23 Brand A
20 Brand B 24 Brand B 24 Brand A 21 Brand B 18 Brand B
a. Determine the probability that a randomly chosen student prefers Brand A.
P(Brand A) = 47/114
b. Determine the probability that one of the students prefers Brand A and is less than 18 years old.
P(Brand A and Age <18) = 7/114
c. Of those students who are less than 18 years old, calculate the probability that a randomly chosen student
prefers (1) B and A and (2) Brand B.
P(Brand A if Age <18) = 6/114
P(Brand B if Age <18) = 6/114
P(Brand A if Age≥18) = 34/114
P(Brand B if Age≥18) = 38/114
d. Of those students who are at least 18 years old, calculate the probability that a randomly chosen student
prefers (1) Brand A and (2) Brand B.
P(Brand A if Age ≥18) = 38/114
P(Brand B if Age≥18) = 42/114
A selection of soft-drink users is asked to taste the two disguised soft drinks and indicate which they prefer. The accompanying data contains the results of a simulated challenge on a college campus.
Age Preference Age Preference Age Preference Age Preference Age Preference Age Preference
17 Brand B 21 Brand A 21 Brand B 19 Brand A 21 Brand A 18 Brand B
19 Brand A 16 Brand A 18 Brand B 23 Brand B 19 Brand B 22 Brand B
21 Brand A 20 Brand A 21 Brand A 24 Brand A 19 Brand A 22 Brand B
19 Brand B 19 Brand A 16 Brand A 19 Brand A 20 Brand B 21 Brand A
18 Brand A 19 Brand A 19 Brand B 21 Brand B 18 Brand A
24 Brand B 21 Brand B 23 Brand A 20 Brand A 20 Brand B
22 Brand A 18 Brand A 17 Brand B 22 Brand B 20 Brand A
20 Brand A 20 Brand A 19 Brand B 21 Brand B 17 Brand B
22 Brand B 22 Brand A 24 Brand A 22 Brand B 21 Brand B
19 Brand B 19 Brand A 20 Brand A 21 Brand B 20 Brand A
16 Brand A 24 Brand A 24 Brand A 22 Brand B 17 Brand B
16 Brand A 21 Brand B 16 Brand B 18 Brand B 21 Brand A
21 Brand B 22 Brand A 18 Brand B 22 Brand B 16 Brand A
22 Brand B 21 Brand B 22 Brand B 20 Brand B 16 Brand A
22 Brand B 20 Brand A 19 Brand B 19 Brand B 23 Brand B
19 Brand B 19 Brand A 22 Brand A 19 Brand B 20 Brand B
24 Brand B 22 Brand A 23 Brand B 23 Brand B 21 Brand A
17 Brand A 21 Brand A 16 Brand B 22 Brand A 23 Brand A
20 Brand B 24 Brand B 24 Brand A 21 Brand B 18 Brand B
a. Determine the probability that a randomly chosen student prefers Brand A.
P(Brand A) = 47/114
b. Determine the probability that one of the students prefers Brand A and is less than 18 years old.
P(Brand A and Age <18) = 7/114
c. Of those students who are less than 18 years old, calculate the probability that a randomly chosen student
prefers (1) B and A and (2) Brand B.
P(Brand A if Age <18) = 6/114
P(Brand B if Age <18) = 6/114
P(Brand A if Age≥18) = 34/114
P(Brand B if Age≥18) = 38/114
d. Of those students who are at least 18 years old, calculate the probability that a randomly chosen student
prefers (1) Brand A and (2) Brand B.
P(Brand A if Age ≥18) = 38/114
P(Brand B if Age≥18) = 42/114
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