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A gambler bets one dollar in each game. She wins two dollars with probability 0.3, one dollar with probability 0.2 and zero dollar with probability

A gambler bets one dollar in each game. She wins two dollars with probability 0.3, one dollar with probability 0.2 and zero dollar with probability 0.5. Please use Chebyshev's inequality, the central limit theorem and the Chernoff bound to estimate the probability that she is ahead after 400 games.

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