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Witty_Username

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  1. The total of $77k includes the $50k to pay for Precaution A, plus the expected value of the contingency, which is $27k (90% x 30% x $100k). It is interesting that there is no single scenario in which the contractor will actually experience a cost of $77k. Either they will pay the $50k for precaution A and then contingency either won't occur, or will cost $0, in which case their total cost will be only $50k, or they will pay the $50k and have bad luck anyway and still experience the $100k contingency, in which case their cost is $150k. Only if they run the scenario multiple times will they all average out to $77k in the long run.
  2. It looks to me like an expected value problem. In the scenario with no precaution the expected value is the chance of the contingency occurring, times the expected value if it does occur, so .9*(1*100,000)=90,000. Precaution A gives an expected value of 50,000+(.9*(.3*100,000))=77,000 Precuation B gives an expected value of 75,000+(.9*(.1*100,000))=84,000 Since the scenario with the lowest expected value is Precaution A, I would allow the contractor to price the contingency at a maximum of $77,000.
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