An insurance company categorizes its policyholders into three mutually exclusive groups: high-risk, medium-risk, and low-risk. An internal study of the company showed that 45% of the policyholders are low-risk and 35% are medium-risk. The probability of death over the next year, given that a policyholder is high-risk is two times the probability of death of a medium-risk policyholder. The probability of death over the next year, given that a policyholder is medium-risk is three times the probability of death of a low-risk policyholder. The probability of death of a randomly selected policyholder, over the next year, is 0.009.

Calculate the probability of death of a policyholder over the next year, given that the policyholder is high-risk.

• 0.0025
• 0.0200
• 0.1215
• 0.2000
• 0.3750

An insurance company studies back injury claims from a manufacturing company. The insurance company finds that 40% of workers do no lifting on the job, 50% do moderate lifting and 10% do heavy lifting.

During a given year, the probability of filing a claim is 0.05 for a worker who does no lifting, 0.08 for a worker who does moderate lifting and 0.20 for a worker who does heavy lifting.

A worker is chosen randomly from among those who have filed a back injury claim. Calculate the probability that the worker’s job involves moderate or heavy lifting.

• 0.75
• 0.81
• 0.85
• 0.86
• 0.89

A student takes an examination consisting of 20 true-false questions. The student knows the answer to [math]N[/math] of the questions, which are answered correctly, and guesses the answers to the rest. The conditional probability that the student knows the answer to a question, given that the student answered it correctly, is 0.824. Calculate [math]N[/math]

• 8
• 10
• 14
• 16
• 18

An actuary analyzed historical auto and home insurance data and has concluded the following:

• The probability that a policyholder with only home coverage reports a claim is 3%
• The probability that a policyholder with only car coverage reports a claim is 5%
• The probability that a policyholder with both home and car coverage reports a claim is 6%
• 60% of policyholders holding car or home coverage have car coverage and 70% have home coverage

Determine the probability that a policyholder holds car insurance coverage, given that the policyholder reported a claim.

• 4/15
• 4/9
• 0.6471
• 2/3
• 11/15

Suppose we have six risks. The probability that the [math]n[/math]^th risk's claim frequency equals [math]i[/math] is [math]1/(n+1)[/math] for [math] i = 0, \ldots, n [/math]. A risk is randomly selected with each risk equally likely to be selected. If a samples claim frequency of 4 is observed for the selected risk, determine the probability that a new sample claim frequency for the selected risk equals 0.

• 0.1283
• 0.1631
• 0.1731
• 0.391
• 0.4083

An insurer sells two types of policies. The claim frequency for a single coverage period for each type policy is given below:

A type of policy is randomly selected with type A being three times as likely to be selected as type B. If a sample claim frequency equalling 2 is observed for the selected policy type, what is the probability that a new sample claim frequency is less than 2 for the selected policy type.

1. 0.57
2. 0.6
3. 0.6563
4. 0.6818
5. 0.7

An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3.

Calculate the probability that a woman has none of the three risk factors, given that she does not have risk factor A.

• 0.280
• 0.311
• 0.467
• 0.484
• 0.700

The following information is given about a group of high-risk borrowers.

1. Of all these borrowers, 30% defaulted on at least one student loan.
2. Of the borrowers who defaulted on at least one car loan, 40% defaulted on at least one student loan.
3. Of the borrowers who did not default on any student loans, 28% defaulted on at least one car loan.

A statistician randomly selects a borrower from this group and observes that the selected borrower defaulted on at least one student loan.

Calculate the probability that the selected borrower defaulted on at least one car loan.

• 0.33
• 0.40
• 0.44
• 0.65
• 0.72

A health insurer sells policies to residents of territory X and territory Y. Past claims experience indicates the following:

1. 20% of the total policyholders from territory X and territory Y combined filed no claims.
2. 15% of the policyholders from territory X filed no claims.
3. 40% of the policyholders from territory Y filed no claims.

Calculate the probability that a randomly selected policyholder was a resident of territory X, given that the policyholder filed no claims.

• 0.09
• 0.27
• 0.50
• 0.60
• 0.80

The following information is given about a group of high-risk borrowers.

1. Of all these borrowers, 30% defaulted on at least one student loan.
2. Of the borrowers who defaulted on at least one car loan, 40% defaulted on at least one student loan.
3. Of the borrowers who did not default on any student loans, 28% defaulted on at least one car loan.

A statistician randomly selects a borrower from this group and observes that the selected borrower defaulted on at least one student loan.

Calculate the probability that the selected borrower defaulted on at least one car loan.

• 0.33
• 0.40
• 0.44
• 0.65
• 0.72