A bank classifies borrowers as "high risk" or "low risk," and23% of its loans are made to those in the "high risk" category. Ofall the bank's loans, 8% are in default. It is also known that 46%of the loans in default are to high-risk borrowers. Let H representthe event that a randomly selected loan is issued to a "high risk"borrower. Let D be the event that a randomly selected loan is indefault. Round your answers to 4 decimal places. Your workfor this entire problem will be hand-graded, see instructionsbelow.
a. What is the probability that a randomlyselected loan is in default and issued to a high-risk borrower?
b. What is the probability that a loan willdefault, given that it is issued to a high-risk borrower?
c. What is the probability that a randomlyselected loan is either in default or issued to a high-riskborrower?
d. A loan is being issued to a borrower who isnot high-risk. What is the probability that this loan willdefault?
e. Are events D and H independent? Justify theanswer.
Yes, because P(D) ? P(H)
Yes, because P(H | D) > P(H) + P(D)
No, because P(D ? H) ? P(D) × P(H)
No, because P(D | H) ? P(H)
Not enough information to determine
