Question

A retail establishment accepts either the American Express or the VISA credit card. A total of 24 percent of its customers carry an American Express card, 61 percent carry a VISA card, and 11 percent carry both cards. What percentage of its customers carry a credit card that the establishment will accept?

Answer 1

By applying the principle of inclusion-exclusion, we find that 74% of the retail establishment's customers carry a credit card that the establishment will accept.

Step-by-step explanation:

To calculate the percentage of a retail establishment's customers who carry a credit card that the establishment will accept, we can use the principle of inclusion-exclusion for two sets, where the sets are the customers carrying an American Express card and the customers carrying a VISA card.

Using the given numbers: 24% of customers carry an American Express card, 61% carry a VISA card, and 11% carry both.

The formula for the principle of inclusion-exclusion is: Total = (American Express + VISA) - (Both).

So, we calculate the percentage as follows: (24 + 61) - 11 = 85 - 11 = 74%.

Therefore, 74% of the retail establishment's customers carry a credit card that the establishment will accept.

Answer 2

The answer is: 74% of its customers carry a credit card the store will accept.

Step-by-step explanation:

• Let A denote the event a customer carries American Express credit card (24%)
• Let V denote the event a customer carries Visa credit card (61%)
• Let AV denote the event a customer carries both credit cards (11%)

P(A ∪ V) = probability that a customer carries at least one credit card

P(A ∪ V) = P(A) + P(V) − P(AV)

P(A ∪ V) = 0.24 + 0.61 − 0.11 = 0.74