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 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

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 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

An actuary studied the likelihood that different types of drivers would be involved in at least one collision during any one-year period. The results of the study are:

Given that a driver has been involved in at least one collision in the past year, calculate the probability that the driver is a young adult driver.

• 0.06
• 0.16
• 0.19
• 0.22
• 0.25

The probability that a randomly chosen male has a blood circulation problem is 0.25. Males who have a blood circulation problem are twice as likely to be smokers as those who do not have a blood circulation problem.

Calculate the probability that a male has a blood circulation problem, given that he is a smoker.

• 1/4
• 1/3
• 2/5
• 1/2
• 2/3

A study of automobile accidents produced the following data:

An automobile from one of the model years 2014, 2013, and 2012 was involved in an accident. Calculate the probability that the model year of this automobile is 2014.

• 0.22
• 0.30
• 0.33
• 0.45
• 0.50

In a group of health insurance policyholders, 20% have high blood pressure and 30% have high cholesterol. Of the policyholders with high blood pressure, 25% have high cholesterol. A policyholder is randomly selected from the group.

Calculate the probability that a policyholder has high blood pressure, given that the policyholder has high cholesterol.

• 1/6
• 1/5
• 1/4
• 2/3
• 5/6