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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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