edu-2009-fall-p-sols

edu-2009-fall-p-sols - SOCIETY OF ACTUARIES/CASUALTY...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY P SAMPLE EXAM SOLUTIONS Copyright 2009 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. PRINTED IN U.S.A. Page 1 of 62
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1. Solution: D Let event that a viewer watched gymnastics event that a viewer watched baseball event that a viewer watched soccer G B S = = = Then we want to find () () () () ( ) ( ) ( ) ( ) Pr 1 Pr 1P r P r P r P r P r P r P r 1 0.28 0.29 0.19 0.14 0.10 0.12 0.08 1 0.48 0.52 c GBS GBSG BG SB SG B S ⎡⎤ ∪∪ =− ⎣⎦ + + ∩ − ∩ + ∩ ∩ = ++−−−+ = −= -------------------------------------------------------------------------------------------------------- 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 [ ] [ ] [ ] [ ] [] [ ] [ ] '' ' PA B PA PB PA B PA B PA PB ∪= + + Then add these two equations to get [ ] [ ] [ ] [ ] [ ] ( ) [ ] [ ] ( ) ( ) [] [] '2 ' ' 0.7 0.9 2 1 ' 1.6 2 1 0.6 PA B PA B PA PB PB P A B A B ∪+ = + + ∩+ += + =+ = Page 2 of 62
Background image of page 2
4. Solution: A () () [] 12 For 1, 2, let event that a red ball is drawn form urn event that a blue ball is drawn from urn . Then if is the number of blue balls in urn 2, 0.44 Pr[ ] Pr[ ] Pr i i i Ri Bi x R RB B R R B B = = = == + = ∩∪∩ [][] [][] Pr Pr Pr Pr 41 6 6 10 16 10 16 Therefore, 32 3 3 32 2.2 16 16 16 2.2 35.2 3 32 0.8 3.2 4 RR BB x xx x x x + ⎛⎞ =+ ⎜⎟ ++ ⎝⎠ + =+= + += + = = -------------------------------------------------------------------------------------------------------- 5. Solution: D Let N(C) denote the number of policyholders in classification C . Then N(Young Female Single) = N(Young Female) – N(Young Female Married) = N(Young) – N(Young Male) – [N(Young Married) – N(Young Married Male)] = 3000 – 1320 – (1400 – 600) = 880 . -------------------------------------------------------------------------------------------------------- 6. Solution: B Let H = event that a death is due to heart disease F = event that at least one parent suffered from heart disease Then based on the medical records, 210 102 108 937 937 937 312 625 937 937 c c PH F PF ⎡⎤ ∩= = ⎣⎦ and 108 108 625 | 0.173 937 937 625 c c c PHF = = Page 3 of 62
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon