Question

A new Superman Mastercard has been issued to 2000 customers. Of these, 1500 hold a Visa card, 500 hold an American Express card, and 40 hold both a Visa and an American Express. Find the probability that a customer chosen at random holds a Visa card, given the customer holds an American Express card.

a. 0.06
b. 0.08
c. 0.10
d. 0.12

Answer 1

To find the probability that a customer chosen at random holds a Visa card, given that the customer holds an American Express card, we can use conditional probability. The probability is 0.08.

Step-by-step explanation:

Given that a customer holds an American Express card, we want to find the probability that the customer also holds a Visa card. To do this, we can use the formula for conditional probability:

P(Visa | American Express) = P(Visa and American Express) / P(American Express)

First, we calculate the number of customers who hold both a Visa and American Express card, which is 40. Next, we calculate the number of customers who hold an American Express card, which is 500. Finally, we plug these values into the formula to find:

P(Visa | American Express) = 40 / 500 = 0.08

Therefore, the probability that a randomly chosen customer, who holds an American Express card, also holds a Visa card is 0.08. Hence, the answer is option b. 0.08.