In order to boost retention and recruitment, a restaurant owner has decided to offer its employees health, dental and vision insurance to its employees. Each employee is eligible for health insurance but can only choose one of vision or dental insurance. The owner has compiled the following enrolment information:

• 15% of employees opted out of any insurance coverage
• 70% of employees enrolled for health insurance coverage
• 35% of employees enrolled for health but not vision
• 10% of employees enrolled for dental but not health

Determine the percentage of employees who enrolled in vision but not dental.

1. 0.25
2. 0.3
3. 0.35
4. 0.38
5. 0.4

A University is hosting its annual actuarial alumni event that will host 150 people. You are given the following about the attendees:

• 75 have the ASA designation
• 50 have the FSA designation
• 35 have the ACAS designation
• 30 have the FCAS designation
• 90 have two designations
• None of the attendees have more than two designations

The ASA designation is required to get the FSA designation and the ACAS designation is required to get the FCAS designation. Determine the number of attendees who are associates (ASA or ACAS) but not fellows (FSA or FCAS).

• 15
• 20
• 25
• 30
• 40

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

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

Determine the number of claims reported in the year 2018 and 2021 combined.

• 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:

• 80% are in phase III or higher
• 60% are in phase III or lower
• 30% are in phase II or phase IV

Determine the percentage of the company's drugs that are in phase I or phase III of the FDA approval process

• 30%
• 40%
• 50%
• 60%
• 70%

A survey of a group’s viewing habits over the last year revealed the following information:

1. 28% watched gymnastics
2. 29% watched baseball
3. 19% watched soccer
4. 14% watched gymnastics and baseball
5. 12% watched baseball and soccer
6. 10% watched gymnastics and soccer
7. 8% watched all three sports.

Calculate the percentage of the group that watched none of the three sports during the last year.

• 24%
• 36%
• 41%
• 52%
• 60%

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

You are given

• [math]\operatorname{P}[A \cup B] = 0.7[/math]
• [math]\operatorname{P}[A \cup B'] = 0.9[/math]

Calculate [math]\operatorname{P}[A] [/math].

• 0.2
• 0.3
• 0.4
• 0.6
• 0.8

An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44.

Calculate the number of blue balls in the second urn.

• 4
• 20
• 24
• 44
• 64

An auto insurance company has 10,000 policyholders. Each policyholder is classified as

1. young or old;
2. male or female; and
3. married or single.

Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young married males.

Calculate the number of the company’s policyholders who are young, female, and single.

• 280
• 423
• 486
• 880
• 896

An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year and 60% of policyholders who have only a homeowners policy will renew next year. The company estimates that 80% of policyholders who have both an auto policy and a homeowners policy will renew at least one of those policies next year.

Company records show that 65% of policyholders have an auto policy, 50% of policyholders have a homeowners policy, and 15% of policyholders have both an auto policy and a homeowners policy.

Using the company’s estimates, calculate the percentage of policyholders that will renew at least one policy next year.

• 20%
• 29%
• 41%
• 53%
• 70%