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You have one million $, but for some reason want to earn an additional $50. Your...

You have one million $, but for some reason want to earn an additional $50. Your strategy is to play roulette at a casino, and always bet $1 on black, until you own $1,000,050.

What is the probability that you will be successful?

Hint: The probability of black in a single game is p = 18/38 . Prove a recursion relation for the probability Pn of finishing at $1,000,050, starting with $n.

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