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For a fundraiser, there is a raffle with 125125 tickets. One ticket will win a $270\$270 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____

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Q. For a fundraiser, there is a raffle with 125125 tickets. One ticket will win a $270\$270 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____
  1. Calculate Probability of Winning: Calculate the probability of winning the prize. Probability of winning P(win)P(\text{win}) = Number of winning tickets / Total number of tickets = 1125\frac{1}{125}.
  2. Calculate Probability of Not Winning: Calculate the probability of not winning the prize. Probability of not winning P(not win)P(\text{not win}) = Number of non-winning tickets / Total number of tickets = 124125\frac{124}{125}.
  3. Determine Winning Ticket Amount: Determine the amount won for the winning ticket.\newlineAmount won for winning ticket = $270\$270.
  4. Determine Non-Winning Ticket Amount: Determine the amount won for a non-winning ticket. Amount won for non-winning ticket = $0\$0.
  5. Calculate Expected Payoff for Winning Ticket: Calculate the expected payoff for a winning ticket.\newlineExpected payoff for winning = P(win)×Amount won for winning ticket=1125×$(270)P(\text{win}) \times \text{Amount won for winning ticket} = \frac{1}{125} \times \$(270).
  6. Calculate Expected Payoff for Non-Winning Ticket: Calculate the expected payoff for a non-winning ticket.\newlineExpected payoff for non-winning = P(not win)×Amount won for non-winning ticket=124125×$0P(\text{not win}) \times \text{Amount won for non-winning ticket} = \frac{124}{125} \times \$0.
  7. Add Expected Payoffs for Total: Add the expected payoffs to get the total expected payoff.\newlineTotal expected payoff = Expected payoff for winning + Expected payoff for non-winning = 1125∗$(270)\frac{1}{125} * \$(270) + 124125∗$(0)\frac{124}{125} * \$(0).
  8. Perform Calculations for Total Expected Payoff: Perform the calculations to find the total expected payoff.\newlineTotal expected payoff = 1125∗$(270)\frac{1}{125} * \$(270) + 00 = \$\(2.16\).

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