The table below shows the soft drink preferences of people in three age groups (

Question

The table below shows the soft drink preferences of people in three age groups (255 subjects total).

a) If one of the 255 subjects is randomly selected, find the probability that the person drinks cola given that this person is under 21 years of age.

b) If one of the 255 subjects is randomly selected, find the probability that the person is under 21 years of age given that this person drinks cola.

c) If one of the 255 subjects is randomly selected, find the probability that this person is between 21 and 40 given that this person does not drink cola.

Cola Root Beer Lemon-Lime Under 21 years of age 40 25 20 between 21 to 40 35 20 30 over 40 years of age 20 30 35

Explanation / Answer

Following table shows the row total and column total:

a)

Out of 85 subjects under 21 years of age, 40 persons drink cola is

P(drink cola | under 21 years of age) = 40 /85 = 0.4706

b)

Out of 95 subjects drink cola, 40 are under 21 years of age is

P(under 21 years of age|drink cola) = 40 /95 = 0.4211

c)

Out of 75 +85 = 160 subjects, 20+30 = 50 subjects are between 21 and 40 so the probability that this person is between 21 and 40 given that this person does not drink cola is

P(between 21 and 40 | does not drink cola) = 50 / 160 = 0.3125

Cola Root Beer Lemon-Lime Total Under 21 years of age 40 25 20 85 between 21 to 40 35 20 30 85 over 40 years of age 20 30 35 85 Total 95 75 85 255

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