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There is a game where the outcome is a random integer from 11 to 2020. If the outcome is even, you win $15\$15. If the outcome is odd, you win nothing. If you play the game, what is the expected payoff?\newline$\$____

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Q. There is a game where the outcome is a random integer from 11 to 2020. If the outcome is even, you win $15\$15. If the outcome is odd, you win nothing. If you play the game, what is the expected payoff?\newline$\$____
  1. Calculate Probability of Winning: question_prompt: What is the expected payoff for playing the game where even numbers win $15\$15 and odd numbers win nothing?\newline Step 11: Calculate the probability of winning. There are 1010 even numbers between 11 and 2020, so the probability of winning is 1020\frac{10}{20} or 12\frac{1}{2}.
  2. Calculate Expected Payoff: Step 22: Calculate the expected payoff. The expected payoff is the probability of winning multiplied by the amount won per win. So, Expected Payoff = (Probability of Winning)×(Amount Won per Win)(\text{Probability of Winning}) \times (\text{Amount Won per Win}).
  3. Plug in Values: Step 33: Plug in the values to calculate the expected payoff. Expected Payoff = (12)×$15(\frac{1}{2}) \times \$15.
  4. Find Expected Payoff: Step 44: Do the math to find the expected payoff. Expected Payoff = $7.50\$7.50.

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