SOA/CAS Exam P Sample Questions - The Online Test Page

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$Name: Quiz 5 Math 100 Fall 2011 1. (10 pts.) Consider the equation ...$

7. An insurance company estimates that 40% of policyholders who have only an auto policywill renew next year and 60% of policyholders who have only a homeowners policy willrenew next year. The company estimates that 80% of policyholders who have both anauto 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% ofpolicyholders have a homeowners policy, and 15% of policyholders have both anauto and a homeowners policy.Using the company’s estimates, calculate the percentage of policyholders that willrenew at least one policy next year.(A) 20(B) 29(C) 41(D) 53(E) 70Page 6 of 82
8. Among a large group of patients recovering from shoulder injuries, it is found that 22%visit both a physical therapist and a chiropractor, whereas 12% visit neither of these.The probability that a patient visits a chiropractor exceeds by 0.14 the probability thata patient visits a physical therapist.Determine the probability that a randomly chosen member of this group visits aphysical therapist.(A) 0.26(B) 0.38(C) 0.40(D) 0.48(E) 0.629. An insurance company examines its pool of auto insurance customers and gathers thefollowing information:(i)(ii)(iii)(iv)All customers insure at least one car.70% of the customers insure more than one car.20% of the customers insure a sports car.Of those customers who insure more than one car, 15% insure asports car.Calculate the probability that a randomly selected customer insures exactly one car andthat car is not a sports car.Page 7 of 82
Page 1 and 2: SOCIETY OF ACTUARIES/CASUALTY ACTUA
Page 3 and 4: 2. The probability that a visit to
Page 5: (A) 280(B) 423(C) 486(D) 880(E) 896
Page 9 and 10: 11. An actuary studying the insuran
Page 11 and 12: What is the probability that a woma
Page 13 and 14: 16. An insurance company determines
Page 15 and 16: (A) 0.38(B) 0.47(C) 0.68(D) 0.84(E)
Page 17 and 18: 21. Upon arrival at a hospital’s
Page 19 and 20: 24. The number of injury claims per
Page 21 and 22: 27. A study of automobile accidents
Page 23 and 24: 30. An actuary has discovered that
Page 25 and 26: 33. The loss due to a fire in a com
Page 27 and 28: 37. The lifetime of a printer costi
Page 29 and 30: Calculate C.(A) 0.1(B) 0.3(C) 0.4(D
Page 31 and 32: 43. A company takes out an insuranc
Page 33 and 34: 46. A device that continuously meas
Page 35 and 36: (A) 85(B) 163(C) 168(D) 213(E) 2555
Page 37 and 38: (A) 0.031(B) 0.066(C) 0.072(D) 0.11
Page 39 and 40: 56. An insurance policy is written
Page 41 and 42: 59. An insurer's annual weather-rel
Page 43 and 44: 63. The warranty on a machine speci
Page 45 and 46: 66. A company agrees to accept the
Page 47 and 48: (A) 161(B) 165(C) 173(D) 182(E) 250
Page 49 and 50: 4(A)2y8(B)3/2y8(C)3y(D)16y1024(E)5y
Page 51 and 52: (D)(E)102r52 2 r75. The monthly pro
Page 53 and 54: 78. A device runs until either of t
Page 55 and 56: 82. An insurance company issues 125
Page 57 and 58:
85. The total claim amount for a he
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88. The waiting time for the first
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91. An insurance company insures a
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95. X and Y are independent random
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98. Let X 1 , X 2 , X 3 be a random
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(A) 0.47(B) 0.58(C) 0.83(D) 1.42(E)
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104. A joint density function is gi
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107. Let X denote the size of a sur
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Calculate⎡ 1⎤P⎢Y < X X =⎣ 3
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113. Two life insurance policies, e
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116. An actuary determines that the
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119. An auto insurance policy will
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⎧ 1 2⎪ ( 10 − xy ) for 2 ≤
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SOCIETY OF ACTUARIES/CASUALTY ACTUA
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4. Solution: AFor i = 1, 2, letRi=
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9. Solution: BLetM = event that cus
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14. Solution: Ak1 11 1 1 1 ⎛1⎞p
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19. Solution: BApply Bayes’ Formu
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25. Solution: BLet Y = positive tes
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31. Solution: DLet X denote the num
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36. Solution: BTo determine k, note
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41. Solution: ELetX = number of gro
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44. Solution: CIf k is the number o
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5( ) ⎤ = ∑ ( ) Pr[ = ]E⎡⎣f
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54. Solution: BLet Y denote the cla
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59. Solution: BThe distribution fun
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64. Solution: ALet X denote claim s
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68. Solution: CNote that X has an e
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74. Solution: EFirst note R = 10/T
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( X < ) ∪ ( Y < )Pr ⎡⎣1 1 ⎤
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40 − 3n−2≥nTo find such an n,
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-----------------------------------
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92. Solution: BLet X and Y denote t
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⎧ 1⎪ , 0< t1 < 6 , 0< t2 < 6 ,
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99. Solution: C2We use the relation
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105. Solution: AThe calculation req
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228= Var[ X + Y] = E⎡( X + Y) ⎤
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111. Solution: E3 f ( 2, y)Pr ⎡
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116. Solution: DDenote the number o
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120. Solution: AWe are given that X
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