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

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

(A) 0.324(B) 0.657(C) 0.945(D) 0.950(E) 0.99526. The probability that a randomly chosen male has a circulation problem is 0.25 . Maleswho have a circulation problem are twice as likely to be smokers as those who do nothave a circulation problem.What is the conditional probability that a male has a circulation problem, given that he isa smoker?(A)(B)(C)(D)(E)1413251223Page 20 of 82
27. A study of automobile accidents produced the following data:ModelyearProportion ofall vehiclesProbability ofinvolvementin an accident1997 0.16 0.051998 0.18 0.021999 0.20 0.03Other 0.46 0.04An automobile from one of the model years 1997, 1998, and 1999 was involvedin an accident.Determine the probability that the model year of this automobile is 1997 .(A) 0.22(B) 0.30(C) 0.33(D) 0.45(E) 0.5028. A hospital receives 1/5 of its flu vaccine shipments from Company X and the remainderof its shipments from other companies. Each shipment contains a very large number ofvaccine vials.Page 21 of 82
Page 1 and 2: SOCIETY OF ACTUARIES/CASUALTY ACTUA
Page 3 and 4: 2. The probability that a visit to
Page 5 and 6: (A) 280(B) 423(C) 486(D) 880(E) 896
Page 7 and 8: 8. Among a large group of patients
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: 24. The number of injury claims per
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
Page 59 and 60: 88. The waiting time for the first
Page 61 and 62: 91. An insurance company insures a
Page 63 and 64: 95. X and Y are independent random
Page 65 and 66: 98. Let X 1 , X 2 , X 3 be a random
Page 67 and 68: (A) 0.47(B) 0.58(C) 0.83(D) 1.42(E)
Page 69 and 70: 104. A joint density function is gi
Page 71 and 72:
107. Let X denote the size of a sur
Page 73 and 74:
Calculate⎡ 1⎤P⎢Y < X X =⎣ 3
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113. Two life insurance policies, e
Page 77 and 78:
116. An actuary determines that the
Page 79 and 80:
119. An auto insurance policy will
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⎧ 1 2⎪ ( 10 − xy ) for 2 ≤
Page 83 and 84:
SOCIETY OF ACTUARIES/CASUALTY ACTUA
Page 85 and 86:
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
Page 127 and 128:
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
Page 135 and 136:
120. Solution: AWe are given that X
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