This year, a medical insurance policyholder has probability 0.70 of having no emergency room visits, 0.85 of having no hospital stays, and 0.61 of having neither emergency room visits nor hospital stays

Calculate the probability that the policyholder has at least one emergency room visit and at least one hospital stay this year.

• 0.045
• 0.060
• 0.390
• 0.667
• 0.840

The probability that a member of a certain class of homeowners with liability and property coverage will file a liability claim is 0.04, and the probability that a member of this class will file a property claim is 0.10. The probability that a member of this class will file a liability claim but not a property claim is 0.01.

Calculate the probability that a randomly selected member of this class of homeowners will not file a claim of either type.

• 0.850
• 0.860
• 0.864
• 0.870
• 0.890

An actuary compiles the following information from a portfolio of 1000 homeowners insurance policies:

1. 130 policies insure three-bedroom homes.
2. 280 policies insure one-story homes.
3. 150 policies insure two-bath homes.
4. 30 policies insure three-bedroom, two-bath homes.
5. 50 policies insure one-story, two-bath homes.
6. 40 policies insure three-bedroom, one-story homes.
7. 10 policies insure three-bedroom, one-story, two-bath homes.

Calculate the number of homeowners policies in the portfolio that insure neither one-story nor two-bath nor three-bedroom homes.

• 310
• 450
• 530
• 550
• 570

A profile of the investments owned by an agent’s clients follows:

1. 228 own annuities.
2. 220 own mutual funds.
3. 98 own life insurance and mutual funds.
4. 93 own annuities and mutual funds.
5. 16 own annuities, mutual funds, and life insurance.
6. 45 more clients own only life insurance than own only annuities.
7. 290 own only one type of investment (i.e., annuity, mutual fund, or life insurance).

Calculate the agent’s total number of clients.

• 455
• 495
• 496
• 500
• 516

A policyholder purchases automobile insurance for two years. Define the following events:

F = the policyholder has exactly one accident in year one.

G = the policyholder has one or more accidents in year two. Define the following events:

1. The policyholder has exactly one accident in year one and has more than one accident in year two.
2. The policyholder has at least two accidents during the two-year period.
3. The policyholder has exactly one accident in year one and has at least one accident in year two.
4. The policyholder has exactly one accident in year one and has a total of two or more accidents in the two-year period.
5. The policyholder has exactly one accident in year one and has more accidents in year two than in year one.

Determine the number of events from the above list of five that are the same as [math]F \cap G [/math].

• None
• Exactly one
• Exactly two
• Exactly three
• All

Insurance company examines its pool of auto insurance customers and gathers the following information:

1. All customers insure at least one car.
2. 64% of the customers insure more than one car.
3. 20% of the customers insure a sports car.
4. Of those customers who insure more than one car, 15% insure a sports car.

Calculate the probability that a randomly selected customer insures exactly one car, and that the car is not a sports car.

• 0.16
• 0.19
• 0.26
• 0.29
• 0.31

The annual numbers of thefts a homeowners insurance policyholder experiences are analyzed over three years.

Define the following events:

1. A = the event that the policyholder experiences no thefts in the three years.
2. B = the event that the policyholder experiences at least one theft in the second year.
3. C = the event that the policyholder experiences exactly one theft in the first year.
4. D = the event that the policyholder experiences no thefts in the third year.
5. E = the event that the policyholder experiences no thefts in the second year, and at least one theft in the third year.

Determine which three events satisfy the condition that the probability of their union equals the sum of their probabilities.

• Events A, B, and E
• Events A, C, and E
• Events A, D, and E
• Events B, C, and D
• Events B, C, and E

In a certain group of cancer patients, each patient's cancer is classified in exactly one of the following five stages: stage 0, stage 1, stage 2, stage 3, or stage 4.

1. 75% of the patients in the group have stage 2 or lower.
2. 80% of the patients in the group have stage 1 or higher.
3. 80% of the patients in the group have stage 0, 1, 3, or 4.

One patient from the group is randomly selected.

Calculate the probability that the selected patient's cancer is stage 1.

• 0.20
• 0.25
• 0.35
• 0.48
• 0.65

A survey of 100 TV viewers revealed that over the last year:

1. 34 watched CBS.
2. 15 watched NBC.
3. 10 watched ABC.
4. 7 watched CBS and NBC.
5. 6 watched CBS and ABC.
6. 5 watched NBC and ABC.
7. 4 watched CBS, NBC, and ABC.
8. 18 watched HGTV, and of these, none watched CBS, NBC, or ABC.

Calculate how many of the 100 TV viewers did not watch any of the four channels (CBS, NBC, ABC or HGTV).

• 1
• 37
• 45
• 55
• 82

A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses.

Calculate the probability that the next mattress sold is either king or queen-size

• 0.12
• 0.15
• 0.80
• 0.85
• 0.95