A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labeled A,B,and C. The consumers are classified according to age and package design preference. If one of these consumers is randomly selected and prefers design B,what is the probability that the person is 25 or older?
A) 0.28
B) 0.14
C) 0.45
D) 0.27
E) 0.78

Question

A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labeled A,B,and C. The consumers are classified according to age and package design preference.  If one of these consumers is randomly selected and prefers design B,what is the probability that the person is 25 or older?
A) 0.28 
B) 0.14 
C) 0.45 
D) 0.27 
E) 0.78

Quizplus · Accepted Answer

We need to use Bayes' theorem to compute this probability:

P(25 or older | design B) = P(25 or older and design B) / P(design B)

We can obtain the numerator from the table: there are 40 consumers who are 25 or older and prefer design B.

To compute the denominator, we need to sum up the number of consumers who prefer design B across age groups:

P(design B) = (45+40+25)/200 = 0.55

Therefore,

P(25 or older | design B) = (40/200) / 0.55 = 0.45

So the probability that a consumer who prefers design B is 25 or older is 0.45.

A Market Research Firm Is Investigating the Appeal of Three