Answer:
There is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.
Step-by-step explanation:
Number of customers having a Visa card = 1,500
Number of customers having an American Express card = 500
Number of customers having Visa and American Express card = 75
Total number of customers = 1,500 + 500 = 2,000
We are asked to find the probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.
This problem is related to conditional probability which is given by
For the given problem it becomes
The probability P(VISA and AE) is given by
P(VISA and AE) = 75/2000
P(VISA and AE) = 0.0375
The probability P(AE) is given by
P(AE) = 500/2000
P(AE) = 0.25
Finally,
Therefore, there is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.