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You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 11 to 2020. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is even, you win $18\$18. If the number the ball lands on is odd, you win nothing. If you play the game, what is the expected payoff?\newline$\$____

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Q. You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 11 to 2020. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is even, you win $18\$18. If the number the ball lands on is odd, you win nothing. If you play the game, what is the expected payoff?\newline$\$____
  1. Question Prompt: question_prompt: What is the expected payoff for playing the game with the wheel?
  2. Total Wheel Sections: There are 2020 sections on the wheel, so there are 2020 possible outcomes.
  3. Number of Even Numbers: Half of the numbers from 11 to 2020 are even, which means there are 1010 even numbers.
  4. Probability of Winning: If the ball lands on an even number, you win $18\$18. So the probability of winning $18\$18 is 1010 out of 2020, or 12\frac{1}{2}.
  5. Calculate Expected Payoff: To find the expected payoff, multiply the amount won (18)bytheprobabilityofwinning(18) by the probability of winning (\frac{11}{22}$).
  6. Final Expected Payoff: Expected payoff = \(\$18 \times \frac{1}{2}\)
  7. Final Expected Payoff: Expected payoff = \(\$18 \times \frac{1}{2}\) Expected payoff = \(\$9\)

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