Q. 2.9 - A First Course in Probability

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?

Step-by-Step Solution

Answer

The percentage of customers carrying a credit card that the establishment will accept is $74\%$.

Step 1. Given information.

It is given that,

Probability of customers carrying an American Express card $P\left(A\right)=0.24$

Probability of customers carrying a VISA Express card $P\left(B\right)=0.61$

Probability of customers carrying both cards $P(A\cap B)=0.11$

Step 2. Find the percentage of customers carrying a credit card that the establishment will accept.

The percentage of customers carrying a credit card that the establishment will accept is $=A\cup B$

$$\begin{gathered} P(A\cup B)=P\left(A\right) + P\left(B\right) - P\left(A\cap B\right) \\ =0.24 + 0.61 - 0.11 \\ = 0.74 \end{gathered}$$

Therefore, the percentage of customers carrying a credit card that the establishment will accept is $74\%$.