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Find expected payoffs


An insurance company offers flood insurance to customers in a certain area. Suppose they charge dollar sign, 500 for a given plan. Based on historical data, there is a 1, percent 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 dollar sign, 10, comma, 000.
Here is a table that summarizes the possible outcomes from the company's perspective:
EventPayoutNet gain left parenthesis, X, right parenthesis
Flooddollar sign, 10, comma, 000minus, dollar sign, 9, comma, 500
No flooddollar sign, 0dollar sign, 500
Let X represent the company's net gain from one of these plans.
Calculate the expected net gain E, left parenthesis, X, right parenthesis.
E, left parenthesis, X, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text