Example Suppose A, B, C fail on demand independently with probability 0.1 each T OR AND AND University of Strathclyde Business School T= ^ た = (A.B) What is the probability of the top A B A event T? 01 0.1 0-1 Probability of Top Event Exact P(T) = P(A.B) + P(A.C) − P((A.B).(A.C)) = = P(A.B) + P(A.C) – P(A.B.C) = 0.019 Rare event approximation P(T) = P(A.B) + P(A.C) = P(A).P(B)+P(A).P(C) = 0.02 University of Strathclyde Business School A
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- 4) Suppose John is risk neutral and faces an uncertain outcome in which he loses $ 1000 $1000 with probability p and $0 with probability (1-p) (1-p), and John knows the value of p. John is offered insurance. John's value of this insurance is \40, i.e. his maximum willingness to pay for the insurance is $40. What is the value of p with 0Jamal has a utility function U= w!/2_where W is his wealth in millions of dollars and Uis the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. Graph Jamal's utility function. Is he risk averse? Explain. b. Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (Hint:The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) c. 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