Question

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 customers as they check 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 by 1000 customers over a one-week period. The data set is in the file MarketBasket, and it contains the following variables for each customer:

- Bread—wheat, white, or none
- Jelly—grape, strawberry, or none
- Peanut butter—creamy, natural, 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 |

which means that customer 1 purchased white bread, grape jelly, and no peanut butter. The second record is

white |
strawberry |
none |

which means that customer 2 purchased white bread, strawberry jelly, and no peanut butter. The sixth record in the data set is

none |
none |
none |

which means that the sixth customer did not purchase bread, jelly, or peanut butter.

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 (10 points/question):

- The probability that a random customer does not purchase any of the three products (bread, jelly, or peanut butter).
- The probability that a random customer purchases white bread.
- The probability that a random customer purchases wheat bread.
- The probability that a random customer purchases grape jelly given that he or she purchases white bread.
- The probability that a random customer purchases strawberry jelly given that he or she purchases white bread.
- The probability that a random customer purchases creamy peanut butter given that he or she purchases white bread.
- The probability that a random customer purchases natural peanut butter given that he or she purchases white bread.
- The probability that a random customer purchases creamy peanut butter given that he or she purchases wheat bread.
- The probability that a random customer purchases natural peanut butter given that he or she purchases wheat bread.
- The probability that a random customer purchases white bread, grape jelly, and creamy peanut butter.

Bread |
Jelly |
Peanut Butter |

white | grape | none |

white | strawberry | none |

none | none | none |

white | none | none |

wheat | none | none |

none | none | none |

none | none | none |

wheat | none | none |

white | grape | none |

white | grape | creamy |

white | strawberry | none |

none | none | none |

none | none | none |

white | grape | creamy |

white | grape | none |

white | grape | none |

none | none | none |

none | none | creamy |

none | none | none |

Answer #1

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 analysing, 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 thishe 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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