Question

1500 customers hold a VISA card; 500 hold an American Express card; and, 75 hold a VISA and an American Express. What is the probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card?

Answer 1

Answer:

There is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.

$P(VISA \:| \:AE) = 15\%$

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

$P(A \:| \:B) = \frac{P(A \:and \:B)}{P(B)}$

For the given problem it becomes

$P(VISA \:| \:AE) = \frac{P(VISA \:and \:AE)}{P(AE)}$

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,

$P(VISA \:| \:AE) = \frac{P(VISA \:and \:AE)}{P(AE)}\\\\P(VISA \:| \:AE) = \frac{0.0375}{0.25}\\\\P(VISA \:| \:AE) = 0.15\\\\P(VISA \:| \:AE) = 15\%$

Therefore, there is 15% probability that a customer chosen at random holds a VISA card, given that the customer has an American Express card.