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You are playing a game that involves flipping a coin, but you begin to suspect that...

You are playing a game that involves flipping a coin, but you begin to suspect that the coin is not fair (P(heads) = P(tails) = 0.5). In fact, your current estimate of P(heads) = 0.59, based on 100 coin flips. Is this enough information to say that the coin is not fair with 95% confidence? If not, how many more coin flips would be required (assuming the P(heads) remains the same)?

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