Question: The following table gives numbers of claims at a large insurance company by kind and by geographic region.

                                     East           South          Midwest          West

Hospitalization                   75           128               29               52

Physician's visit                233           514              104             251

Outpatient treatment        100           326               65               99

Compute column totals and row totals. What do they mean?

a. If a bill is chosen at random, what is the probability that it is from the Midwest?

b. What is the probability that a randomly chosen bill is from the East?

c. What is the probability that a randomly chosen bill is either from the Midwest or from the South? What is the relation between these two events?

d. What is the probability that a randomly chosen bill is for hospitalization?

e. Given that a bill is for hospitalization, what is the probability that it is from the South?

f. Given that a bill is from the East, what is the probability that it is for a physician's visit?

g. Given that a bill is for outpatient treatment, what is the probability that it is from the West?

h. What is the probability that a randomly chosen bill is either from the East or for outpatient treatment (or both)?

i. What is the probability that a randomly selected bill is either for hospitalization or from the South (or both)?