> All that statistics gives you is the probability of having a result at least this extreme with an unbiased coin.
If you subscribe to frequentist statistics and use the null hypothesis of "coin is not biased", yes. But if you're a Bayesian you can compute the probability that the coin bias is greater than a given amount.
Granted. But in either case, there's no proof - only a probability that you haven't reached an incorrect conclusion. I associate the concept of proof with logical certainty, and no statistical method will give you that.
If you subscribe to frequentist statistics and use the null hypothesis of "coin is not biased", yes. But if you're a Bayesian you can compute the probability that the coin bias is greater than a given amount.