10. A bank classifies borrowers as high risk or low risk. Only 15% of its loans are madeto those in the high-risk category. Of all its loans, 5% are in default, and 40% of those indefault were made to high-risk borrowers. What is the probability that a high-riskborrower will default?

P(high risk) = 0.15P(default ) = 0.05P(Hugh risk |default) = 0.40

Answered: 10. A bank classifies borrowers as high…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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8. Assume that an insurance company knows the following probabilities relating to automobile accidents (where the second column refers to the probability that the policyholder has at least one accident during the annual policy period): Age of Driver 16 - 25 26 - 50 51 - 65 66 - 90 Probability of Accident 0.05 0.02 0.03 0.04 Fraction of Company's Insured Drivers 0.10 0.55 0.20 0.15 A randomly selected driver from the company's insured drivers has an accident. What is the conditional probability that the driver is in the 16-25 age group?
Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest to Moria. Based on past experience, the probability of surviving such a quest is 84.3%. If BIC charges a premium of 7,703 silver coins and would pay a death benefit of 35,029 silver coins if the insured were to die, what is the expected value of this insurance policy to BIC?
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A company prices its tornado insurance using the following assumptions:• In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.11. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 12-year period.
A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.13. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 10-year period.
Historical data suggests that one in four of all insurance policies of a certain company are surrendered before maturity. Assume that 15 policies are randomly selected from the company's database. What is the probability that the number of surrendered policies are not more than one?
A person invests $3 in a market in which he may gain $1 with probability or may lose $1 with probability in a period independently. • What is the probability that the person ever goes broke? • What is the expected time periods to go broke?
There is a 0.9987 probability that a randomly selected 32 year old male lives through the year. A life insurance company charges $183 for insuring that the male will live through the the year. If the male does not survive the year, the policy pays out $80,000 as a death benefit. a. From the perspective of the 32 year old male, what are the monetary values corresponding to the two events of surviving the year and not surviving ? b. If the 32 year old male purchases the policy, what is his expected value? c. Can the insurance company expect to make a profit from many such policies? Yes or no because the insurance company expects to make an average profit of $___ on every 32 year old male it insured for 1 year.
11.
On average, 10 people per hour conduct transactions at a special services desk in a commercial bank.what is the probability that more than 15 people will wish to conduct transactions at the special services desk during a particular hour?
A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.11. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 11-year period.
Assume that there is a 66% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on fourfour independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is (Round to four decimal places as needed.) b. With fourfour hard disk drives, the probability that catastrophe can be avoided is (Round to six decimal places as needed.)

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10. A bank classifies borrowers as high risk or low risk. Only 15% of its loans are made to those in the high-risk category. Of all its loans, 5% are in default, and 40% of those in default were made to high-risk borrowers. What is the probability that a high-risk borrower will default?