Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist.

Calculate the probability that a randomly chosen member of this group visits a physical therapist.

• 0.26
• 0.38
• 0.40
• 0.48
• 0.62

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

1. All customers insure at least one car.
2. 70% 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 car is not a sports car.

• 0.13
• 0.21
• 0.24
• 0.25
• 0.30

An actuary studying the insurance preferences of automobile owners makes the following conclusions:

1. An automobile owner is twice as likely to purchase collision coverage as disability coverage.
2. The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage.
3. The probability that an automobile owner purchases both collision and disability coverages is 0.15.

Calculate the probability that an automobile owner purchases neither collision nor disability coverage.

• 0.18
• 0.33
• 0.48
• 0.67
• 0.82

An insurer offers a health plan to the employees of a large company. As part of this plan, the individual employees may choose exactly two of the supplementary coverages A, B, and C, or they may choose no supplementary coverage. The proportions of the company’s employees that choose coverages A, B, and C are 1/4, 1/3, and 5/12 respectively. Calculate the probability that a randomly chosen employee will choose no supplementary coverage

• 0
• 47/144
• 1/2
• 97/144
• 7/9

An insurance agent offers his clients auto insurance, homeowners insurance and renters insurance. The purchase of homeowners insurance and the purchase of renters insurance are mutually exclusive. The profile of the agent’s clients is as follows:

1. 17% of the clients have none of these three products.
2. 64% of the clients have auto insurance.
3. Twice as many of the clients have homeowners insurance as have renters insurance.
4. 35% of the clients have two of these three products.
5. 11% of the clients have homeowners insurance, but not auto insurance.

Calculate the percentage of the agent’s clients that have both auto and renters insurance.

• 7%
• 10%
• 16%
• 25%
• 28%

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

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

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

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

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