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There is a game where the outcome is a random integer from 11 to 5050. If the outcome is odd, you win $14\$14. If the outcome is even, you win nothing. If you play the game, what is the expected payoff?\newline$\$____

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Q. There is a game where the outcome is a random integer from 11 to 5050. If the outcome is odd, you win $14\$14. If the outcome is even, you win nothing. If you play the game, what is the expected payoff?\newline$\$____
  1. Prompt: question_prompt: What's the expected payoff for playing the game where odd numbers win $14\$14 and even numbers win $0\$0?
  2. Total Outcomes: There are 5050 possible outcomes, half odd and half even. So there are 2525 odd numbers and 2525 even numbers from 11 to 5050.
  3. Probability Calculation: The probability of getting an odd number is 2550\frac{25}{50}, which simplifies to 12\frac{1}{2}.
  4. Expected Payoff Calculation: The expected payoff for an odd number is $14\$14 times the probability of getting an odd number. So, $14×(12)\$14 \times \left(\frac{1}{2}\right).
  5. Final Expected Payoff: Calculating the expected payoff: $14×(12)=$7\$14 \times \left(\frac{1}{2}\right) = \$7.

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