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Find expected payoffs


An insurance company offers flood insurance to customers in a certain area. Suppose they charge $500 for a given plan. Based on historical data, there is a 1% probability that a customer with this plan suffers a flood, and in those cases, the average payout from the insurance company to the customer was $10,000.
Here is a table that summarizes the possible outcomes from the company's perspective:
EventPayoutNet gain (X)
No flood$0$500
Let X represent the company's net gain from one of these plans.
Calculate the expected net gain E(X).
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi