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There is a game where the outcome is a random integer from 11 to 100100. If the outcome is odd, you win $13\$13. If the outcome is even, you win nothing. If you play the game, what is the expected payoff?\newline$\$____

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Q. There is a game where the outcome is a random integer from 11 to 100100. If the outcome is odd, you win $13\$13. If the outcome is even, you win nothing. If you play the game, what is the expected payoff?\newline$\$____
  1. Prompt: question_prompt: What's the expected payoff for playing the game where odd numbers win $13\$13 and even numbers win nothing?
  2. Odd Numbers: There are 100100 possible outcomes, and half of them are odd. So there are 5050 odd numbers between 11 and 100100.
  3. Total Odd Winnings: Each odd number wins $13\$13, so the total winnings for all odd outcomes is 50×$1350 \times \$13.
  4. Calculate Total Winnings: Calculate the total winnings for odd outcomes: $\(50\) \times (\$\(13\)) = (\$\(650\)).
  5. Calculate Expected Payoff: To find the expected payoff, divide the total winnings by the number of possible outcomes. Use the formula \(\frac{\text{total winnings}}{\text{number of possible outcomes}}\).
  6. Calculate Expected Payoff: To find the expected payoff, divide the total winnings by the number of possible outcomes. Calculate the expected payoff: \(\$650 \div 100 = \$6.50\).

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