Chapter 4.4, Problem 37E

Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit and credit) cards in making purchases (Associated Press, January 16, 2006). The results of the study provided the following probabilities.

• The probability that a consumer uses a plastic card when making a purchase is .37.
• Given that the consumer uses a plastic card, there is a .19 probability that the consumer is 18 to 24 years old.
• Given that the consumer uses a plastic card, there is a .81 probability that the consumer is more than 24 years old.

U.S. Census Bureau data show that 14% of the consumer population is 18 to 24 years old.

1. a. Given the consumer is 18 to 24 years old, what is the probability that the consumer uses a plastic card?
2. b. Given the consumer is over 24 years old, what is the probability that the consumer uses a plastic card?
3. c. What is the interpretation of the probabilities shown in parts (a) and (b)?
4. d. Should companies such as Visa, MasterCard, and Discover make plastic cards available to the 18 to 24 year old age group before these consumers have had time to establish a credit history? If no, why? If yes, what restrictions might the companies place on this age group?