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A raffle has 1,0001,000 tickets. One ticket will win a $820\$820 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____

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Q. A raffle has 1,0001,000 tickets. One ticket will win a $820\$820 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____
  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 = 11000\frac{1}{1000}
  2. Calculate Probability of Losing: Calculate the probability of winning nothing.\newlineProbability of winning nothing = Number of losing tickets / Total number of tickets\newlineProbability of winning nothing = 9991000\frac{999}{1000}
  3. Determine Expected Payoff for Winning: Determine the expected payoff for winning the prize.\newlineExpected payoff for winning = Probability of winning ∗* Prize amount\newlineExpected payoff for winning = 11000\frac{1}{1000} ∗* $820\$820\newlineExpected payoff for winning = $0.82\$0.82
  4. Determine Expected Payoff for Losing: Determine the expected payoff for winning nothing.\newlineExpected payoff for winning nothing = Probability of winning nothing ×\times Prize amount for losing\newlineExpected payoff for winning nothing = 9991000×$0\frac{999}{1000} \times \$0\newlineExpected payoff for winning nothing = $0\$0
  5. Calculate Total Expected Payoff: Calculate the total expected payoff.\newlineTotal expected payoff = Expected payoff for winning + Expected payoff for winning nothing\newlineTotal expected payoff = $0.82\$0.82 + $0\$0\newlineTotal expected payoff = $0.82\$0.82

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