1. Using cross tabulation, construct a contingency table for the variables Region and Control. This table will have raw frequencies and totals from the database. Next divide each cell value and row/column total by the total number in the table, thereby producing a joint probability table from the resulting proportions. Explore various probabilities that might exist if a business analyst were to randomly select a hospital from the database. Some examples might be:
a. The probability that the hospital is from the Pacific region and is under Government Non Federal control.
b. The probability that the hospital is a Other Nonprofit hospital given that it is from the Mountain region.
c. The probability that the hospital is Investor Owned For Profit.

2. Construct a contingency table for the variables Control and Service. From this table and the resultant joint probability table, explore various probabilities that might exist if a business analyst were to randomly select a hospital from the database. Some examples might be:
a. The probability that the hospital is a children's hospital if it is known that the hospital is Other Non Profit.
b. The probability that it is a Non Government Non Profit hospital or is a psychiatric hospital.
c. The probability that it is a General Medical and Surgery hospital and is Investor Owned For Profit.

3. Construct a contingency table for the variables Region and Service. From this table and the resultant joint probability table, identify at least one marginal, one union, one intersection, and one conditional probability and briefly explain what each means to someone who is mining the data.