Suppose a bridge has 10 toll booths in the east-bound lane: four are only for E-Z Pass holders, two are only for exact change, one takes only tokens, and the remainder are manned by toll collectors who accept only cash. During heavy-traffic hours it is difficult to see the signs indicating the type of toll booth. Suppose a driver selects a toll booth randomly.

• a. What is the probability that an exact-change toll booth is selected?

• b. What is the probability that a manual-collection toll booth or the token toll booth is selected?

• c. What is the probability that an E-Z Pass toll booth is not selected?

• d. Suppose the driver has only tokens. What is the probability of selecting the appropriate toll booth?

The following data represent the probability distribution of the holding period returns for an investment in Lazy Rapids Kayaks (LARK) stock. State of the Economy Scenario #(s) Probability, p(s) HPR Boom 1 0.324 30.80% Normal growth 2 0.396 8.90% Recession 3 0.28 -18.00% a. What is the expected return on LARK? (Round your answer to 2 decimal places.) Expected return % b. What is the standard deviation of the returns on LARK? (Round your answer to 2 decimal places.) Standard deviation %

The following data represent the probability distribution of the holding period returns for an investment in Lazy Rapids Kayaks (LARK) stock.

a. What is the expected return on LARK? (Round your answer to 2 decimal places.)

Expected return               %

b. What is the standard deviation of the returns on LARK? (Round your answer to 2 decimal places.)

Standard deviation              %

Per IFRS, a contingent item with a probability of 65% would be considered to be:

Select one:

a. Probable

b. More than probable

c. A provision

d. Less than probable

The probability that a FEDEX delivery man meets someone at a random home to sign for a delivery that requires signature is 80%. If FEDEX delivery men call at 9 random homes to make such a delivery what is the probability that

(a) people are at home to sign in one or six homes

(b) people are at home to sign in exactly 8 homes

(c) People are at home to sign in more than 3 homes.

For a life insurance company, it is important to construct life tables (consisting of the probability that a person will survive in the next year, conditional on a person that has been survived up to current). A life insurance company uses life tables to assist calculation of life insurance premium. Assume that the lifetime of randomly selected person is approximately normally distributed with a mean 68 years and a standard deviation 4 year.

a) A whole life insurance implies that insurance company needs to pay out the death benefit if the insured die, no matter when the death event is happened.  For a group of 10 independent newborn insureds who are currently all under whole life insurances, what is the probability that at least 9 death benefits will be paid after 75 years.

b) What is the probability that a randomly selected person will survive beyond 75 years?

c)A whole life insurance implies that insurance company needs to pay out the death benefit if the insured die, no matter when the death event is happened.  For a group of 10 independent newborn insureds who are currently all under whole life insurances, What is the probability that a randomly selected person will die before 60 years?

Amy’s income is $ 10,000 and she is risk averse. The probability of someone slipping on her sideway is 1/8. If this happens, she will be sued for $5,000 and will have to pay that amount. She can purchase insurance at a price of $0.2 per dollar of coverage. Show how the equilibrium amount of insurance coverage is determined. If her utility of money is given as U=m^0.5, where m is the money amount in a particular state, calculate the optimal insurance.