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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Exam 1 Solution September 24, 2009 Answers: V1: ECDAB EADCD V2: DACCD EEEDA 1. A doctor is studying the relationship between high blood pressure and heartbeat abnormalities in her patients. She tests a random sample of her patients and nds that: 40% have high blood pressure; of those with high blood pressure, 60% have an irregular heartbeat; of those with an irregular heartbeat, 80% have high blood pressure. For a randomly chosen person, What portion of the patients selected have an irregular heartbeat? Answer: 30% De ne events : H=high blood pressure, I=irregular heartbeat. P [ H ] = 40% , P [ I  H ] = 60% , thus P [ I ∩ H ] = P [ H ] · P [ I  H ] = 24% ; P [ H  I ] = P [ I ∩ H ] P [ I ] = 24% P [ I ] = 80% , thus P [ I ] = 30% . 2. An insurance agent o ers his clients auto insurance, homeowners insurance and life insurance. The purchases of the three products are mutuall y independent . The pro le of the agent's clients is as follows: 55% of the clients have auto insurance; 45% of the clients have homeowners insurance; 60% of the clients have life insurance. Calculate the percentage of the agent's clients that have more than one insurance product. Answer: 55 De ne three events as A, H and L. P [ A ] = 55% , P [ H ] = 45% , P [ L ] = 60% . The required probability is N 4 + N 5 + N 6 + N 7 = P [ A ∩ H ∩ L ]+ P [ A ∩ H ∩ L ]+ P [ A ∩ H ∩ L ]+ P [ A ∩ H ∩ L ] . Since the three events are mutually independent, P [ A ∩ H ∩ L ] = 0 . 55 · . 45 · (1 . 6) = 0 . 099 , P [ A ∩ H ∩ L ] = (1 . 55) · . 45 · . 6 = 0 . 1215 , P [ A ∩ H ∩ L ] = 0 . 55...
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 Fall '08
 Yang,Y
 Conditional Probability, Probability, Probability theory

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