Question

The ABC Bank's process for approving business loans has two steps: First document screening, in which the information provided on the loan application is checked and compared with the bank's minimum standards. If a loan application passes the document screening, the second step is a meeting with the borrower's CEO and CFO. If the application does not pass the document screening, the request is rejected without having a meeting. In the bank's experience, only 40% of all business loan applications pass the document screening and of those that do pass, 80% pass the meeting and are granted loans. Let D represent the event that a loan application passes document screening. Let M represent the event that the application passes the meeting. Find the following

a. P(D)

b. P(not D)

c. P(M ∩ D)

d. P(M)

e. Events D and M are (pick one): statistically independent / mutually exclusive / neither f. Describe the meaning of P(not M | D) in English. (Don't leave the symbols D and M in your description; replace them with words.)

Answer 1

P(D) = 0.4
P(M|D) = 0.8

a)
P(D) = 0.4

b)
P(not D) = 1 - P(D) = 1 - 0.4 = 0.6

c)
P(M and D) = P(M|D) * P(D)
= 0.8 * 0.4
= 0.32

d)
P(M) = 0.8

e)
Neither

f)
P(not M | D) = Probability of loan is not granted given that the loan application is passed