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At a carnival, there is a raffle with 100100 tickets. One ticket will win a $990\$990 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____

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Q. At a carnival, there is a raffle with 100100 tickets. One ticket will win a $990\$990 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____
  1. Calculate Probability of Winning: Calculate the probability of winning the prize.\newlineProbability of winning = Number of winning tickets / Total number of tickets\newlineProbability of winning = 1100\frac{1}{100}
  2. Calculate Probability of Not Winning: Calculate the probability of not winning the prize.\newlineProbability of not winning = Number of losing tickets / Total number of tickets\newlineProbability of not winning = 99100\frac{99}{100}
  3. Determine Expected Payoff for Winning: Determine the expected payoff for winning.\newlineExpected payoff for winning = Probability of winning ×\times Prize amount\newlineExpected payoff for winning = 1100\frac{1}{100} ×\times $990\$990\newlineExpected payoff for winning = $9.90\$9.90
  4. Determine Expected Payoff for Not Winning: Determine the expected payoff for not winning.\newlineExpected payoff for not winning = Probability of not winning ×\times Prize amount for losing\newlineExpected payoff for not winning = 99100\frac{99}{100} ×\times $0\$0\newlineExpected payoff for not winning = $0\$0
  5. Calculate Total Expected Payoff: Calculate the total expected payoff.\newlineTotal expected payoff = Expected payoff for winning + Expected payoff for not winning\newlineTotal expected payoff = $9.90\$9.90 + $0\$0\newlineTotal expected payoff = $9.90\$9.90

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