In a recent year, business failures in the United States numbered 83,384, according to Dun & Bradstreet. The construction industry accounted for 10,867 of these business failures. The South Atlantic states accounted for 8,010 of the business failures.

Suppose that 1,258 of all business failures were construction businesses located in the South Atlantic states. A failed business is randomly selected from this list of business failures.

a. What is the probability that the business is located in the South Atlantic states?

b. What is the probability that the business is in the construction industry or located in the South Atlantic states?

c. What is the probability that the business is in the construction industry if it is known that the business is located in the South Atlantic states?

d. What is the probability that the business is located in the South Atlantic states if it is known that the business is a construction business?

e. What is the probability that the business is not located in the South Atlantic states if it is known that the business is not a construction business?

f. Given that the business is a construction business, what is the probability that the business is not located in the South Atlantic states?