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There is a raffle with 1,0001,000 tickets. One ticket will win a $270\$270 prize, and the other tickets will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____

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Q. There is a raffle with 1,0001,000 tickets. One ticket will win a $270\$270 prize, and the other tickets will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____
  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 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 = 9991000\frac{999}{1000}
  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 = 11000×$270\frac{1}{1000} \times \$270\newlineExpected payoff for winning = $0.27\$0.27
  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 = 9991000×$0\frac{999}{1000} \times \$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 = $0.27\$0.27 + $0\$0\newlineTotal expected payoff = $0.27\$0.27

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