86.5k views
2 votes
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?

User Tratcher
by
8.6k points

1 Answer

7 votes

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\%\\

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) = (P(A \:and \:B))/(P(B))

For the given problem it becomes


P(VISA \:| \:AE) = (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) = (P(VISA \:and \:AE))/(P(AE))\\\\P(VISA \:| \:AE) = (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.

User Mark Pavlis
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.