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Each cycle a robot turns every coin showing heads to tails, and turns each coin showing tails to heads with probability 50%. After many cycles, what proportion of the coins show heads?

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A stock is at $100 and each day a coin flip moves it up $1 on Heads or down $1 on Tails. What is the probability it is exactly $100 after 10 days?You start with $50 and bet on a sequence of fair coin flips: each head wins you $2 and each tail loses you $1. What is the probability that you eventually run out of money?Write a function to simulate 25 coin flips with 50/50 probability. Return the number of heads.

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