Question

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?

Answer 1

The answer is 1/3 or 0.33

Explanation:

Let's consider the following ocurrences:

A: A person has a MasterCard

B: A person has an American Express

The data says:

P(A∩B) = 0.2

P(A without B) = 0.4

P(B without A) = 0.1

Then, P(A) = P(A∩B) +P(A without B) = 0.2+0.4 = 0.6

By conditional probability theory:

P (B/A) = P(A∩B) / P(A) = 0.2 / 0.6 = 1/3 = 0.33

Thus

P(B/A) = 1/3 = 0.33