An ad agency is developing a campaign to promote a business opening in a new mall development.To develop an appropriate mailing list,they decide to purchase lists of credit card holders from MasterCard and American Express.Combining the lists,they find the following: 40 percent of the people on the list have only a MasterCard and 10 percent have only an American Express card.Another 20 percent hold both MasterCard and American Express.Finally,30 percent of those on the list have neither card.Suppose a person on the list is known to have a MasterCard.What is the probability that person also has an American Express Card?
A).20
B).33
C).18
D).70
E).90

Question

Quizplus · Accepted Answer

We want to find the probability that a person with a MasterCard also has an American Express card. 
Let's first find the total percentage of people on the list who have a MasterCard: 
40% have only a MasterCard + 20% have both MasterCard and American Express = 60%
So, out of 100 people on the list, 60 have a MasterCard.

Now, let's find the percentage of people with a MasterCard who also have an American Express: 
Out of the 60 people with a MasterCard, 20% (or 0.20) have both MasterCard and American Express. So, the probability that a person with a MasterCard also has an American Express is:

(20/100)/(60/100) = 20/60 = 1/3 = 0.33

Therefore, the answer is B) 33.

An Ad Agency Is Developing a Campaign to Promote a Business