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In a game of chance, a player bets \(\dollar 1\) on a single number in a classical roulette wheel numbered from 0 to 36. If the chosen number comes up, the player wins 35 times their bet plus their bet back, receiving a total payout of \(\dollar 36\); otherwise, they lose their bet. In gambling, the gain is defined as the payout minus the cost to play.
  • Calculate the expected gain \(E(X)\) of the player.
  • Interpret the result in terms of the player’s average outcome per game.

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