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Given a coin whose probability of landing on heads was unknown. a guy tossed the coin 1000 times and he got 900 heads. Assuming that each successive coin flip is i.i.d, is it technically correct to refer to the observed value of 90% as 'probability'?

I thought the observed value of 90% can be considered a probability though, after reading a wiki page I'm not so sure.

singularli
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    The answer to this question is a little bit complicated. Your 90% figure "is" a probability, called the "sample probability" or "empirical probability". But it is also "just an estimate" of the "true" probability of getting a heads. You can actually calculate the probability that the estimate is correct, or within a range of values, using statistics, such as using bayes theorem and the likelihood ratio, etc. etc. – nomen Jan 09 '24 at 00:13
  • You might want to look at the law of large numbers. – Ennar Jan 09 '24 at 00:19

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Probability should be seen as an "a priori" measure of the likelihood of an event to occur, while the number of wins out of a given number of attempts is something that approximates the expected result better and better as the number of attempts grows. From the observed outcome of a certain number of attempts you can guess the probability of winning the next try, but you can do even better if you understand the rules of the games and use mathematics (i.e., if you throw a fair die and you know that $52$ times out of $100$ attempts you have previously got an even number, you can wrongly guess that the probability of getting an odd result in the next throw is $0.48$, but this is untrue... while if you know that you have a fair die and you have $\frac{1}{6}$ odds to get a $1$, $\frac{1}{6}$ odds to get a $2$, $\ldots$, $\frac{1}{6}$ odds to get a $6$, you can easily conclude that the probability is $0.5$).

Marco Ripà
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