1. 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. Determine the probability that

a visit to a PCP's office results in both lab work and referral to a specialist.

2. At a water treatment facility, the probability that a random water sample contains

Chemical A and Chemical B is 10%. The probability that a random water sample

contains Chemical A but not Chemical B is 15%. Calculate the probability that a

random water sample contains Chemical A.

3. Of all patients visiting a hospital,

(i) 90% need Medicine A, or Medicine B, or Medicine C.

(ii) 60% need Medicine A.

(iii) 45% need Medicine B.

(iv) 50% need Medicine C.

(v) 30% need both Medicine A and Medicine B.

(vi) 20% need both Medicine B and Medicine C.

(vii) 25% need both Medicine A and Medicine C.

Calculate the probability that a randomly selected patient needs Medicine A, Medicine

B, and Medicine C.

4. An insurance company has three types of annuity products: indexed annuities, fixed

annuities, and variable annuities. You are given:

(a) In a year, 7,000 customers purchase an indexed annuity, 5,000 customers purchase

a fixed annuity, and 6,000 customers purchase a variable annuity.

(b) The number of customers who purchase both an indexed annuity and a variable

annuity is 300 greater than the number of customers who purchase both an

indexed annuity and a fixed annuity.

(c) The number of customers who purchase both an indexed annuity and a variable

annuity is 1,200 greater than the number of customers who purchase both a fixed

annuity and a variable annuity.

(d) 25% of the customers who purchase an indexed annuity and a variable annuity

also purchase a fixed annuity.

(e) 3,800 customers purchase only an indexed annuity.

(f) All customers purchase at least one annuity.

Calculate the number of customers who purchase exactly one type of annuity.

5. 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:

(a) 17% of the clients have none of these three products.

(b) 64% of the clients have auto insurance.

(c) The percentage of clients with homeowners insurance is twice the percentage of

clients with renters insurance.

(d) 35% of the clients have two of these three products.

(e) 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.

6. Under an insurance policy, a maximum of five claims may be filed per year by a

policyholder. Let pn be the probability that a policyholder files n claims during a

given year, where n = 0; 1; 2; 3; 4; 5. An actuary makes the following observations:

(i) pn ? pn+1 for n = 0; 1; 2; 3; 4.

(ii) The difference between pn and pn+1 is the same for n = 0; 1; 2; 3; 4.

(iii) Exactly 40% of policyholders file fewer than two claims during a given year.

Calculate the probability that a random policyholder will file more than three claims

during a given year.

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6. Material selection plays a big role throughout engineering and is especially important in aerospace engineering. The following questions relate to material properties and the use of materials in aerospace applications. (a) State two examples of mechanical properties, other than ductility and brittleness, which can be used in material selection. [1 Mark] (b) State two examples of non-mechanical material properties that can be used in material selection. [1 Mark] [1 Mark] (C) What is the definition of ductility? TURN OVED 6. Material selection plays a big role throughout engineering and is especially important in aerospace engineering. The following questions relate to material properties and the use of materials in aerospace applications. (a) State two examples of mechanical properties, other than ductility and brittleness, which can be used in material selection. [1 Mark] (b) State two examples of non-mechanical material properties that can be used in material selection. [1 Mark] [1 Mark] (C) What is the definition of ductility? TURN OVED

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