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 labelled A, B, and C. The consumers are classified according to age and package design preference. If one of these consumers is randomly selected, what is the probability that the person prefers design A?
A) 0.76
B) 0.38
C) 0.33
D) 0.22
E) 0.39

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 labelled A, B, and C. The consumers are classified according to age and package design preference.  If one of these consumers is randomly selected, what is the probability that the person prefers design A?
A) 0.76 
B) 0.38 
C) 0.33 
D) 0.22 
E) 0.39

Quizplus · Accepted Answer

The table shows that out of the 200 consumers, 108 consumers preferred design A. Therefore, the probability that a randomly selected person prefers design A is 108/200 = 0.54. However, we are only interested in the probability of preference for design A among those who expressed a preference. Looking at the table, we see that 100 + 20 + 12 = 132 consumers expressed a preference for one of the designs. Among those who expressed a preference, 100 preferred design A. Therefore, the probability that a randomly selected person who expressed a preference prefers design A is 100/132 = 0.76.

A Market Research Firm Is Investigating the Appeal of Three