An advertising campaign is being developed to promote a new bookstore opening in the newest mall development.To develop an appropriate mailing list it has been decided to purchase lists of credit card holders from MasterCard and American Express.Combining the lists they find the following: 40% of the people on the list have only a MasterCard and 10% have only an American Express card.Another 20% hold both MasterCard and American Express.Finally,30% 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?

Question

Quizplus · Accepted Answer

We are given that 40% have only a MasterCard, 10% have only an American Express, and 20% have both. That means the percentage of people with a MasterCard is 40% + 20% = 60%. 
We are asked for the probability that a person with a MasterCard also has an American Express. This can be found using conditional probability: 
P(AmEx | MasterCard) = P(AmEx and MasterCard) / P(MasterCard) 
We already know that P(MasterCard) = 60%. To find P(AmEx and MasterCard), we can use the information that 20% have both. So, 
P(AmEx and MasterCard) = 20% 
Substituting these values, we get: 
P(AmEx | MasterCard) = 20% / 60% = 1/3 = 0.33 
Therefore, the answer is B) 33.

An Advertising Campaign Is Being Developed to Promote a New