Answers to Sections 1 and 2 of Marcel B. Finan's "A Probability Course for the Actuaries"
July 19, 2008 by
These answer keys are meant to assist students using Marcel B. Finan's A Probability Course for the Actuaries. With Dr. Finan's permission, Mr. Stolyarov wrote solutions for the problems in his study guide and is endeavoring to make the answer keys to each section publicly available.
You can see his full List of Answer Keys here. Do the problems at the end of each section and then check your answers with these keys.
Dr. Finan's study guide is an excellent resource for those preparing to take Actuarial Exam 1/P on probability.
Problems that require numerical answers are answered here, but it is still the responsibility of the student to provide his or her own work for these problems. These answers are meant to enable students to independently verify the correctness of their reasoning by checking to see if the end result they obtained is correct. Questions from the study guide that require proofs or diagrams are not addressed here, as the end result of those questions is known in advance, and it is the responsibility of the student to provide the procedure for getting there.
Section 1.
Answer 1.1.A={x:x shows a face with prime number}= {2, 3, 5}
Answer 1.2a. HHH, HHT, HTH, HTT, TTT, TTH, THT, THH
Answer 1.2b.
HTT, TTT, TTH, THT
Answer 1.2c. F in set-builder notation is
F={x│x is an element of S with more than one head} = {x|x is an element of S with at least two heads}
Answer 1.3. E={HHH, HHT, HTH, HTT, TTH, THT, THH}. The outcomes with more than one head are, HHH, HHT, HTH. Thus, F={HHH, HHT, HTH,THH}. Thus, F is a subset of E, since F contains only elements that are also in E.
Answer 1.4. There are no elements of E and so E=Ø
Answer 1.9a. 55 tacos
Answer 1.9b. 40 tacos
Answer 1.9c. 10 tacos
Answer 1.10a. 20 students
Answer 1.10b. 5 students
Answer 1.10c. 11 students
Answer 1.10d. 42 students
Answer 1.10e. 46 students
Answer 1.10f. 46 students
Answer 1.11. n(S) = 24
Section 2.
Answer 2.3. (G U B U S)c.
Answer 2.5. There are 880 young, single, female policyholders.
Answer 2.6. 50% of the population owns an automobile or a house, but not both.
Answer 2.7. 5% of visits to a PCP's office result in both lab work and referral to a specialist.
Dr. Finan's study guide is an excellent resource for those preparing to take Actuarial Exam 1/P on probability.
Problems that require numerical answers are answered here, but it is still the responsibility of the student to provide his or her own work for these problems. These answers are meant to enable students to independently verify the correctness of their reasoning by checking to see if the end result they obtained is correct. Questions from the study guide that require proofs or diagrams are not addressed here, as the end result of those questions is known in advance, and it is the responsibility of the student to provide the procedure for getting there.
Section 1.
Answer 1.1.A={x:x shows a face with prime number}= {2, 3, 5}
Answer 1.2a. HHH, HHT, HTH, HTT, TTT, TTH, THT, THH
Answer 1.2b.
HTT, TTT, TTH, THT
Answer 1.2c. F in set-builder notation is
F={x│x is an element of S with more than one head} = {x|x is an element of S with at least two heads}
Answer 1.3. E={HHH, HHT, HTH, HTT, TTH, THT, THH}. The outcomes with more than one head are, HHH, HHT, HTH. Thus, F={HHH, HHT, HTH,THH}. Thus, F is a subset of E, since F contains only elements that are also in E.
Answer 1.4. There are no elements of E and so E=Ø
Answer 1.9a. 55 tacos
Answer 1.9b. 40 tacos
Answer 1.9c. 10 tacos
Answer 1.10a. 20 students
Answer 1.10b. 5 students
Answer 1.10c. 11 students
Answer 1.10d. 42 students
Answer 1.10e. 46 students
Answer 1.10f. 46 students
Answer 1.11. n(S) = 24
Section 2.
Answer 2.3. (G U B U S)c.
Answer 2.5. There are 880 young, single, female policyholders.
Answer 2.6. 50% of the population owns an automobile or a house, but not both.
Answer 2.7. 5% of visits to a PCP's office result in both lab work and referral to a specialist.
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