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There are 5050 cards in a hat, numbered 11 to 5050. The game is to draw one card out of the hat. If the number you draw is even, you win $11\$11. If the number you draw is odd, you win nothing. If you play the game, what is the expected payoff?\newline$\$____

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Q. There are 5050 cards in a hat, numbered 11 to 5050. The game is to draw one card out of the hat. If the number you draw is even, you win $11\$11. If the number you draw is odd, you win nothing. If you play the game, what is the expected payoff?\newline$\$____
  1. Total Cards Distribution: There's 5050 cards, half are even, half are odd. So, 2525 cards are even.
  2. Winning Probability Calculation: If you draw an even card, you win $11\$11. So the chance to win $11\$11 is 2525 out of 5050.
  3. Expected Payoff Calculation: To find the expected payoff, multiply the probability of winning by the amount won: 2550\frac{25}{50} * $11\$11.
  4. Final Payoff Calculation: Do the math: 2550\frac{25}{50} * $11\$11 = 12\frac{1}{2} * $11\$11 = $5.50\$5.50.

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