In problem 2-31, are the events "hospitalization" and "the claim being from the Midwest" independent of each other?
Problem 2-31
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)?