Probability

Piggy Bank is faced with three options which are option A, option B and option C, all these options are a plans to create an incentivize to consumers to acquire Piggy Bank credit cards. From the description provided consumers are likely to make 52 purchases per year. The options are as follows:

Option A- cash back when purchase is made

Option B – cash back when purchase is made from a clothing store

Option C – entry into a draw when consumer makes purchases where 1 in 1,000 consumers will win.

The probability of choosing any option is 1/3, so that the sum probability of all the options is equal to one, therefore we could first construct the probability tree as follows:

Therefore the probability that consumers will choose any of the options is 1/3 and the total probability is equal; to one derived from 1/3 + 1/3 + 1/3 = 1.

In each option however there is a possibility that consumers may like the option or dislike it, we assign a 0.5 probability for the probability that the consumers will like the option and 0.5 probability that consumers will not like the option.

Probability

The probability diagram will then be as follows:

For each option there is 1/3 probability of being chosen by the company, the probability that the consumers will like the option is ½ for each option and this is demonstrated by probability tree above.

Option C however has a certain probability of winning, a consumer has 1/1000 possibility of winning and therefore has 999/1000 of not winning when then consumer makes one purchase, the decision probability tree will therefore be extended as follows:

From the above diagram determine the various probabilities, the following summarizes the probabilities:

The probability that the company chooses option A and the customer likes the option will be determined by multiplying 1/3 X 0.5 = 0.166667, therefore the probability is 0.166667.

The probability that the company chooses option a and the consumer dislikes the option will be determined by 0.16667

Probability

The probability that the company chooses option B and the consumer likes the option will be determined by multiplying both probabilities and this will be 1/3 X 0.5 = 0.166667, therefore the probability is 0.166667

The probability that the company chooses option B and the consumer dislikes the option will be determined by multiplying both probabilities and this will be 1/3 X 0.5 = 0.166667, therefore the probability is 0.166667

The probability that the company chooses option C and the consumer likes and finally that the consumer wins is determined by multiplying 1/3 X 0.5 x 0.001= 0.000167

The probability that the company chooses option C and the consumer dislikes and finally that the consumer wins is determined by multiplying 1/3 X 0.5 x 0.001= 0.000167

The probability that the company chooses option C and the consumer likes and finally that the consumer doe not wins is determined by multiplying 1/3 X 0.5 x 0.999=0.1665

The probability that the company chooses option C and the consumer dislikes and finally that the consumer does not win is 0.1665

Probability

From the above discussion it is evident that option C has lower probability levels, therefore the best option would be either option A or option B because they have a higher possibility of occurrence, it is also evident that option C will need financing of the prizes to the consumers.

## References:

Allan Bluman (2002) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York