edu-2008-spring-p-sols SOA北美精算师资格考试试题 精算师考试复习资料_精品.pdf

SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE SOLUTIONS Copyright 2008 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study note are taken from past SOA/CAS examinations. P-09-08 PRINTED IN U.S.A. Page 1 of 59 1. Solution: D Let G event that a viewer watched gymnastics B event that a viewer watched baseball S event that a viewer watched soccer Then we want to find Pr ⎡⎣(G ∪B ∪S )c ⎤⎦ 1 =−Pr (G ∪B ∪S ) 1 Pr G Pr B Pr S Pr G B Pr G S Pr B S Pr G B S =−⎡ + + − ∩ − ∩ − ∩ + ∩ ∩ ⎤ ⎣ ( ) ( ) ( ) ( ) ( ) ( ) ( )⎦ 1=−(0.28+0.29+0.19−0.14−0.10−0.12+0.08) 1=−0.48 0.52 2. Solution: A Let R = event of referral to a specialist L = event of lab work We want to find P[R∩L] = P[R] + P[L] – P[R∪L] = P[R] + P[L] – 1 + P[~(R∪L)] = P[R] + P[L] – 1 + P[~R∩~L] = 0.30 + 0.40 – 1 + 0.35 = 0.05 . 3. Solution: D First note P A ∪B P A =+P B −P A ∩B [ ] [ ] [ ] [ ] P A ∪B P A =+P B −P A ∩B [ ] [ ] [ ] [ ] Then add these two equations to get P A ∪B +P A ∪B 2P A =+ P B +P B − P A ∩B +P A ∩B [ ] [ ] [ ] ( [ ] [ ]) ( [