A portfolio holds shares of biotechnology companies that are categorized according to their market capitalization as either small cap, mid cap, or large cap. The portfolio consists of 15% small cap, 50% mid cap, and 35% large cap. The probability of bankruptcy in the next five years depends on the market cap of the company: the probability is 30% for small cap, 15% for mid cap, and 5% for large cap.

One of the companies represented in the portfolio is randomly selected. Determine the probability that the randomly selected company is currently classified as mid cap, given that it is assumed to stay in business for the next five years.

• 3/40
• 3/20
• 1/2
• 6/11
• 8/11

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

An insurer sells coverage on two types of risks, type A and type B, with the following loss probabilities:

Assuming both types of risk are equally likely to be selected, determine the probability that the loss will equal to $100 for a randomly selected risk.

• 0.4
• 0.45
• 0.5
• 0.55
• 0.6

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[/math] for [math] i = 0, \ldots, n [/math]. A risk is randomly selected with each risk equally likely to be selected. If a sample 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

A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease.

Calculate the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease.

• 0.115
• 0.173
• 0.224
• 0.327
• 0.514

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

An auto insurance company insures drivers of all ages. An actuary compiled the following statistics on the company’s insured drivers:

A randomly selected driver that the company insures has an accident. Calculate the probability that the driver was age 16-20.

• 0.13
• 0.16
• 0.19
• 0.23
• 0.40

An insurance company issues life insurance policies in three separate categories: standard, preferred, and ultra-preferred. Of the company’s policyholders, 50% are standard, 40% are preferred, and 10% are ultra-preferred. Each standard policyholder has probability 0.010 of dying in the next year, each preferred policyholder has probability 0.005 of dying in the next year, and each ultra-preferred policyholder has probability 0.001 of dying in the next year. A policyholder dies in the next year.

Calculate the probability that the deceased policyholder was ultra-preferred.

• 0.0001
• 0.0010
• 0.0071
• 0.0141
• 0.2817

Upon arrival at a hospital’s emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year:

1. 10% of the emergency room patients were critical;
2. 30% of the emergency room patients were serious;
3. the rest of the emergency room patients were stable;
4. 40% of the critical patients died;
5. 10% of the serious patients died; and
6. 1% of the stable patients died.

Given that a patient survived, calculate the probability that the patient was categorized as serious upon arrival.

• 0.06
• 0.29
• 0.30
• 0.39
• 0.64