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In a raffle, one ticket will win a $100\$100 prize, and the remaining tickets will win nothing. There are 5050 in the raffle. If you have a ticket, what is the expected payoff?\newline$\$____

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Q. In a raffle, one ticket will win a $100\$100 prize, and the remaining tickets will win nothing. There are 5050 in the raffle. If you have a ticket, what is the expected payoff?\newline$\$____
  1. Calculate probability of winning: Calculate the probability of winning the $100\$100 prize.\newlineProbability of winning = Number of winning tickets / Total number of tickets\newlineProbability of winning = 150\frac{1}{50}
  2. Calculate probability of winning nothing: Calculate the probability of winning nothing. Probability of winning nothing = Number of losing tickets / Total number of tickets Probability of winning nothing = 4950\frac{49}{50}
  3. Calculate expected payoff for winning: Calculate the expected payoff for winning the $100\$100 prize.\newlineExpected payoff for winning = Probability of winning ∗* Amount won\newlineExpected payoff for winning = 150\frac{1}{50} ∗* $100\$100\newlineExpected payoff for winning = $2\$2
  4. Calculate expected payoff for losing: Calculate the expected payoff for winning nothing.\newlineExpected payoff for losing = Probability of winning nothing ×\times Amount won for losing\newlineExpected payoff for losing = 4950\frac{49}{50} ×\times $0\$0\newlineExpected payoff for losing = $0\$0
  5. Add expected payoffs to find total: Add the expected payoffs to find the total expected payoff.\newlineTotal expected payoff = Expected payoff for winning + Expected payoff for losing\newlineTotal expected payoff = $2\$2 + $0\$0\newlineTotal expected payoff = $2\$2

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