Question

This question has multiple parts.

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. Data listed below.

a. Determine the probability that a randomly chosen student prefers Brand A.
P(Brand A) =  (Do not use percents. Round to three decimal places as needed.)

b. Determine the probability that one of the students prefers Brand A and is less than 22 years old.
P(Brand A and Age < 22) =  (Do not use percents. Round to three decimal places as needed.)

c. Of those students who are less than 22 years old, calculate the probability that a randomly chosen student prefers (1) Brand A and (2) Brand B.

P(Brand A if Age < 22) =  (Do not use percents. Round to three decimal places as needed.)
P(Brand B if Age < 22) =  (Do not use percents. Round to three decimal places as needed.)

d. Of those students who are at least 22 years old, calculate the probability that a randomly chosen student prefers (1) Brand A and (2) Brand B.

P(Brand A if Age ≥ 22) =  (Do not use percents. Round to three decimal places as needed.)
P(Brand B if Age ≥ 22) =  (Do not use percents. Round to three decimal places as needed.)

Data:

Age	Preference
17	Brand A
18	Brand A
21	Brand A
18	Brand A
17	Brand A
23	Brand B
21	Brand B
20	Brand A
24	Brand B
21	Brand B
18	Brand A
18	Brand A
21	Brand B
21	Brand B
20	Brand B
20	Brand A
24	Brand A
18	Brand B
21	Brand B
21	Brand A
18	Brand B
18	Brand B
20	Brand B
21	Brand A
20	Brand B
18	Brand B
19	Brand A
21	Brand B
19	Brand A
23	Brand A
20	Brand B
24	Brand A
21	Brand B
18	Brand B
20	Brand B
23	Brand A
20	Brand B
23	Brand A
20	Brand B
17	Brand B
19	Brand B
18	Brand A
18	Brand A
21	Brand A
17	Brand B
19	Brand A
22	Brand B
21	Brand B
24	Brand A
17	Brand B
20	Brand B
21	Brand A
18	Brand A
20	Brand B
24	Brand B
16	Brand A
23	Brand A
20	Brand A
21	Brand B
24	Brand A
19	Brand A
23	Brand B
18	Brand A
23	Brand B
20	Brand A
23	Brand A
21	Brand B
21	Brand A
19	Brand B
22	Brand B
19	Brand A
20	Brand A
21	Brand A
22	Brand A
23	Brand B
21	Brand B
21	Brand A
18	Brand B
18	Brand A
21	Brand B
16	Brand B
21	Brand B
21	Brand B
18	Brand A
22	Brand B
22	Brand B
17	Brand A
23	Brand B
17	Brand A
17	Brand A
22	Brand A
19	Brand B
21	Brand B
22	Brand A
17	Brand B
18	Brand B
23	Brand A
20	Brand A
23	Brand A

Answer 1

P(A) = n(E)/n(S)

Where P(A) is the probability of an event A

n(E) is the number of favorable outcomes

n(S) is the total number of events in the sample space.          

a)

There are 49 for Brand A and 50 for Brand B out of a total of 99 voters.

P(A) = 49/99 = 0.495

b)

There are 35 cases where the age is less than 22 and brand is Brand A.

P = 35/99 = 0.356

c)

There are 35 cases of Brand A when age < 22 and 39 cases of Brand B when age < 22 out of a total cases of 74 cases when age < 22.

P(Brand A if Age < 22) = 35/74 = 0.473
P(Brand B if Age < 22) = 39/74 = 0.527

d)

There are 14 cases of Brand A when age >= 22 and 11 cases of Brand B when age >= 22 out of a total cases of 25 cases when age >= 22.

P(Brand A if Age ≥ 22) = 14/25 = 0.560
P(Brand B if Age ≥ 22) = 11/25 = 0.440