You are given the following information about a database of historical claims data:

- 200,000 claims were reported during the years 2018,2019,2020
- 350,000 claims were reported during the years 2019,2020,2021
- 480,000 claims were reported during the years 2018,2019,2020,2021

Determine the number of claims reported in year 2018 or 2021.

- 400,000
- 410,000
- 420,000
- 450,000
- 480,000

A pharmaceutical company has drugs awaiting FDA approval. In order for the FDA to approve a drug for consumer use, the drug must pass through four phases of clinical trials: phase I, II, III, and IV. You are given the following information about the company's drugs that are in the approval process:

- 60% are in phase III or higher
- 60% are in phase III or lower
- 50% are in phase II or phase IV

Determine the percentage of the company's drugs that are in phase I.

- 10%
- 20%
- 30%
- 40%
- 50%

The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35%. Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work. Calculate the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.

- 0.05
- 0.12
- 0.18
- 0.25
- 0.35

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

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

- All customers insure at least one car.
- 64% of the customers insure more than one car.
- 20% of the customers insure a sports car.
- 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 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

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

A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. (For example, a six is three times as probable as a two.) What is the probability of getting an odd number in one throw that is not equal to 1?

- 1/6
- 1/3
- 8/21
- 9/21
- 1/2

**References**

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Let [math]A[/math] and [math]B[/math] be events such that [math]P(A \cap B) = 1/4[/math], [math]P(A^c) = 1/3[/math], and [math]P(B^c) = 1/2[/math]. What is [math]P(A \cup B)[/math]?

- 1/2
- 7/12
- 2/3
- 11/12
- 1

**References**

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

A student must choose one of the subjects, art, geology, or psychology, as an elective. She is equally likely to choose art or psychology and twice as likely to choose geology. What is the probability that the student chooses art or geology?

- 1/2
- 2/3
- 3/4
- 4/5
- 1

**References**

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.