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Out of 500500 tickets in a raffle, one ticket will win a $130\$130 prize. The remaining tickets will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____

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Q. Out of 500500 tickets in a raffle, one ticket will win a $130\$130 prize. The remaining tickets will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____
  1. Calculate Probability: Calculate the probability of winning the prize: 11 winning ticket out of 500500 tickets.\newlineProbability of winning = 1500\frac{1}{500}
  2. Calculate Expected Payoff: Calculate the expected payoff for winning: $130\$130 prize times the probability of winning.\newlineExpected payoff for winning = $130×(1500)\$130 \times \left(\frac{1}{500}\right)
  3. Calculate Expected Payoff: Calculate the expected payoff for not winning: $0\$0 prize times the probability of not winning.\newlineProbability of not winning = 499500\frac{499}{500}\newlineExpected payoff for not winning = $0×(499500)\$0 \times \left(\frac{499}{500}\right)
  4. Add Expected Payoffs: Add the expected payoffs for winning and not winning to get the total expected payoff.\newlineTotal expected payoff = (Expected payoff for winning) + (Expected payoff for not winning)\newlineTotal expected payoff = (130∗(1/500))+(130 * (1/500)) + (00 * (499499/500500))
  5. Simplify Calculation: Simplify the calculation to find the total expected payoff.\newlineTotal expected payoff = $130500+$0\frac{\$130}{500} + \$0\newlineTotal expected payoff = $0.26\$0.26

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