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,what is the probability that the person prefers design A and is under 25?
A) 0.22
B) 0.11
C) 0.18
D) 0.54
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,what is the probability that the person prefers design A and is under 25?
A) 0.22 
B) 0.11 
C) 0.18 
D) 0.54 
E) 0.78

Quizplus · Accepted Answer

Looking at the table, we see that out of the 200 consumers, 38 prefer design A and are under 25. So the probability of randomly selecting one such consumer is: 
P(A and under 25) = 38/200 = 0.19 
However, the question asks for the probability that the person prefers design A AND is under 25, which means we have to consider the intersection of those two events. So the probability we're looking for is the joint probability: 
P(A and under 25) = 0.19 
Therefore, the answer is B) 0.11.

A Market Research Firm Is Investigating the Appeal of Three