Rob’s Market (RM) is a regional food store chain in the southwest United States.
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ROB’S MARKET Rob’s Market (RM) is a regional food store chain in the southwest United States. David White, director of Business Intelligence for RM, would like to initiate a study of the purchase behavior of customers who use the RM loyalty card (a card that customers scan at checkout to qualify for discounted prices). The use of the loyalty card allows RM to capture what is known as “point-of-sale” data, that is, a list of products purchased by a given customer as he/she checks out of the market. David feels that better understanding of which products tend to be purchased together could lead to insights for better pricing and display strategies as well as a better understanding of sales and the potential impact of different levels of coupon discounts. This type of analysis is known as market basket analysis, as it is a study of what different customers have in their “shopping baskets” as they check out of the store. As a prototype study, David wants to investigate customer buying behavior with regard to bread, jelly, and peanut butter. RM’s Information Technology (IT) group, at David’s request, has provided a data set of purchases made by 1000 customers over a one-week period. The data set contains the following variables for each customer: Bread—wheat, white, or none The variables appear in the above order from left to right in the data set, where each row is a customer. For example, the first record of the data set is: white grape none white strawberry none none none none Other records are interpreted in a similar fashion. David would like you to do an initial study of the data to get a better understanding of RM customer behavior with regard to these three products. Managerial Report Prepare a report that gives insight into the purchase behavior of customers who use the RM loyalty card. At a minimum your report should include estimates of the following: 1. The probability that a random customer does not purchase any of the three products (bread, jelly, or peanut butter). 2. The probability that a random customer purchases white bread. 3. The probability that a random customer purchases wheat bread. 4. The probability that a random customer purchases grape jelly given that he/she purchases white bread. 5. The probability that a random customer purchases strawberry jelly given that he/she purchases white bread. 6. The probability that a random customer purchases creamy peanut butter given that he/she purchases white bread. 7. The probability that a random customer purchases natural peanut butter given that he/she purchases white bread. 8. The probability that a random customer purchases creamy peanut butter given that he/she purchases wheat bread. 9. The probability that a random customer purchases natural peanut butter given that he/she purchases wheat bread. 10. The probability that a random customer purchases white bread, grape jelly, and creamy peanut butter. |
Explanation
1.) The probability that a random customer does not purchase any of the three products
=Number of customer does not purchase any of the three products
Number of customer arrived at Rob's Market
= 7 / 19.
2.) The probability that a random customer purchases white bread.
= Number of customer purchased white bread
Number of customer arrived at Rob's Market
= 9 / 19.
3.) The probability that a random customer purchases wheat bread.
= Number of customer purchased wheat bread
Number of customer arrived at Rob's Market
= 2 / 19.
4.) The probability that a random customer purchases grape jelly given that he/she purchases white bread.
=P(customer purchase grape jelly & white bread)
P(customer purchase white bread)
P( A / B) =P(A∩B) / P(B)
=P(A and B) / P(B)
Probability is =6 / 19
9 / 19
= 6 / 9.
5.) The probability that a random customer purchases strawberry jelly given that he/she purchases white bread.
=P(customer purchase strawberry jelly & white bread)
P(customer purchase white bread)
P( A / B) =P(A∩B) / P(B)
=P(A and B) / P(B)
Probability is = 2 / 19
9 / 19
=2 / 9.
6.) The probability that a random customer purchases creamy peanut butter given that he/she purchases white bread.
=P(customer purchase creamy peanut butter & white bread)
P(customer purchase white bread)
P( A / B) =P(A∩B) / P(B)
=P(A and B) / P(B)
Probability is = 2 / 19
9 / 19
=2 / 9.
7.) The probability that a random customer purchases natural peanut butter given that he/she purchases white bread.
=P(customer purchase natural peanut butter & white bread)
P(customer purchase white bread)
Probability is = 0
9 / 19
= 0 ( No customer purchase natural peanut butter )
8.) The probability that a random customer purchases creamy peanut butter given that he/she purchases wheat bread.
=P(customer purchase creamy peanut butter & wheat bread)
P(customer purchase wheat bread)
Probability is = 0
2 / 19
= 0 ( No customer purchase creamy peanut butter with wheat bread )
9.) The probability that a random customer purchases natural peanut butter given that he/she purchases wheat bread.
Similar as problem 7
Since no customer purchase natural peanut butter , therefore intersection probability is also zero.
Therefore this probability is zero.
10.) The probability that a random customer purchases white bread, grape jelly, and creamy peanut butter.
= Number of customers purchase white bread , grape jelly & creamy peanut butter together
Number of customer arrived at Rob's Market
= 2 / 19.
Answer
For this problem basic definition of probability is required and definition of conditional probability is also required.
This problem is also called as market basket analysis in real world as it analyses the data of purchasing of customers in a market or online market. By analyzing, the pattern of purchasing is recorded and according to it, the owner can get help to design his/her products together and can put other offers with it to buy together and due to this customers get access easily to products and get other benefits too.
Conclusions :
1. More customers buy white bread, so David can keep them in large quantities, due to this he will get profit.
2. Less customers buy wheat bread, so David can keep them in small quantity.
3. Many customers buy white bread and grape jelly together, so David can keep them together so he's sale will increase and customers would happy to buy at a same place.
4. Most of the customers don't buy natural peanut butter, here out of 19, no customer bought it, so David can either keep natural peanut butter in very less quantity or don't keep them for sale. Because if he keeps it in very large quantity, he may get loss from it.
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