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# Three options of PiggyBank

The product development team from PiggyBank was convinced by your presentation and has hired you to help them with their credit card decision. They have focused on three options for their credit card incentives:

A. cash back when the consumer makes an online purchase;

B. cash back when the consumer makes a purchase at a clothing store; and

C. entry into a sweepstakes whenever the consumer makes a purchase;

If they choose option C (the sweepstakes entry), they will award a prize to 1 in 1,000 purchases. Based on the frequency that consumers make purchases with their other credit cards, the PiggyBank team estimates that consumers will make an average of 52 purchases a year with the new card.

PiggyBank has asked you about the probability of each option being preferred by card holders. They have also asked the probability of an individual consumer receiving a prize over the course of a year. Share your determination of probability in each of the situations. Explain how these two ways of assessing probability are different and how they can help make decisions.

#### Solution Preview

STEP 1

If they select option C that is the sweepstakes, the award given is 1 in 1,000 purchases. However, there is an average of 52 purchases made by customers every year and this implies that every customer's chance of winning will be (1/1000 + 1/1000 +... + 1/1000)= 52/1000. So the probability will be 0.052, this is the probability that every customer has of winning the sweepstakes during the course of a year. This is also the probability of a customer winning a prize during the course of the year.

STEP 2

The method of calculating the probability of each option being preferred by the cardholders is different. From the entire population of customers there will be percentage of customers who will prefer sweepstakes. These are ...

#### Solution Summary

PiggyBank has been given three options for promoting credit card division. This posting explores these options and helps select the best option.

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