All incentives are dependent on another event occurring meaning that there are about probability which in each option is conditional which implies that an event “EVENT A will occur given the knowledge that EVENT B already occurred. Both events A and B are independen meaning that event A has no effect on the probability of event B occurring (Easton, 1998). In this case one is to determine the probability of each option being preferred by card holders and the probability of a consumer receiving a prize in the course of the year if he has chosen option C.

*Option A: Cash back when a consumer makes an online purchase*

If a consumer chooses to make an online purchase using his card then money is offered back to him as an incentive for using his card to make the purchase. Online shopping is convenient, “has infinite shelf space” and enables the consumer compare product price and features (Hobbs, 1993). Limitations include loss of enjoyment of retail shopping and loss of privacy. Given the above incentive where money is offered back to the consumer after making the purchase online. Probability of this option being preferred by card holders depends mainly on the cardholders themselves and the main question is, are they willing to make purchases online and if so what amount of money is being offered as cash back?

*Option B: Cash back when a consumer makes a purchase at a clothes store*

Since cash is offered back as an incentive for making a purchase at a clothes store this option has the highest degree of conditional probability in because it is only when a card holder makes a purchase at a clothing store then cash is refunded back to him or her. The probability of this option being preferred or chosen by card holders can be calculated as follows:

Take the incentive as “A” and purchase as “B”

Given the two events, A and B probability that event A will occur can be given as follows:

P (B n A) =P (A/B)

So P, (A/B) =P (A n B) / P (B)

P (A n B) and P (B n A) are the same

*Option C: Entry into a sweepstake whenever the consumer makes a purchase*

This option as an incentive can be viewed as having where conditional probability is at its lowest when viewed in the context of how and where the purchase is made because this is not dictated to the card holders by the bank thus purchase can be made anywhere but the probability of this option being chosen by the consumers is also very low because the only event that has to occur is that the card holder has to make 1000 purchases for a prize to be won and it has been estimated that an average of 52 purchases are made in a year for one to win a prize he or she will have to wait for a certain period calculated as follows:

__Number of purchases required / Average number of purchases made in a year__

= 1000/52

=19

This could be viewed by card holders to be costly thus reducing the chances of probability of option C being selected. Probability of an individual consumer receiving a prize in a given year is low because an average of 52 purchases are made in a year and for one to receive a prize 1000 purchases are to be made by the consumer.

The two ways of assessing probability are different because in option B the number of purchases to be made for one to be entitled to cash back is unlimited but in option C a card holder must make 1000 purchases to win a prize.

Consumers are rational in decision making (Kim & Srivastava, 2001) in that they always seek options that favor them. When it comes to probability of choosing any of the above options they will go for the option in which they stand to gain more.

**REFERENCE LIST**** **

Easton, T. (1998). *An Introduction To Probability Theory And Its Application*. New York: Guilford Press.

Kim, N. & Srivastava, H. (2001).*Rationality and decision making, *Michigan: Earthscan

Hobbs, D. (1993) *Doing the Business*. London: Oxford University Press