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?

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.

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.

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.)

5. A manufacturer of cell phones purchases batteries from a vendor. It is not uncommon to receive defective batteries from this vendor, thus whenever a shipment is received, a sample of batteries is inspected. For this month's shipment, a random sample of 280 batteries is selected and each battery is inspected. If the proportion of defective batteries sampled is more than 1.5%, the entire shipment will be returned to the vendor. What is the probability that this month's shipment will be returned if the true proportion of defective batteries is 4%?

7. Suppose that after 10 years of service, 40% of computers have problems withmotherboards (MB), 30% have problems with hard drives (HD), and 15% have problemswith both MB and HD. What is the probability that a 10-year old computer still has fullyfunctioning MB and HD?