The casino game of roulette features 38 colored and numbered pockets on a spinning wheel with a total of 18 red, 18 black, and 2 green pockets. A $1 bet on black wins $1 if the ball falls on black and loses $1 otherwise (i.e., if the ball falls on a red or green pocket). You spin the roulette wheel 10 times, betting on black each time. Use the central limit theorem to find and approximation to the probability that your total winnings after 10 bets are greater than zero.

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