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At a carnival, there is a raffle with 200200 tickets. One ticket will win a $390\$390 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____

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Full solution

Q. At a carnival, there is a raffle with 200200 tickets. One ticket will win a $390\$390 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?\newline$\$____
  1. Multiply and Sum Products: To find the expected payoff, we multiply the value of each outcome by its probability and then sum these products.
  2. Calculate Winning Probabilities: There's a 1200\frac{1}{200} chance to win ($)390(\$)390 and a 199200\frac{199}{200} chance to win ($)0(\$)0.
  3. Calculate Expected Payoff: Expected payoff = (Probability of winning×Prize value)+(Probability of not winning×0)(\text{Probability of winning} \times \text{Prize value}) + (\text{Probability of not winning} \times 0)
  4. Substitute Values: Expected payoff = 1200∗$$\frac{1}{200} * \$\$390390) + \left(\frac{199199}{200200} * $\$00\right)
  5. Simplify Expression: Expected payoff = $390200+0\frac{\$390}{200} + 0
  6. Final Expected Payoff: Expected payoff = $1.95\$1.95

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