# Does it make sense to speak of probability of a hidden outcome? (context: confidence intervals) [duplicate]

My question is concerning the frequentist approach to probability. Assume that you tossed a coin but don't see the outcome. Does it make sense to say that it shows head with a probability of 0.5? Or doesn't it make sense to say that because it either is or is not heads?

I would argue that it does make sense because otherwise you would not be allowed to e.g. speak about the probability of your opponent in poker holding a certain combination of cards (he either has them or not...) which is clearly nonsensical. This would mean that at the end what counts is not whether something is or is not but your knowledge about the fact. But perhaps this is an axiomatic issue?

This would also have profound consequences for the interpretation of confidence intervals. You are always told that you are not allowed to say that there is a 95% probability that e.g. the true mean is within the interval because it either is or is not - so no probability here.

But in case you are allowed to speak of probabilities of hidden outcomes you would also be allowed to say that the true mean is within the confidence interval with 95% probability. Or am I mistaken?

• Hi vonjd - perhaps you could edit to emphasize the differences this question has from the potential duplicate we were discussing. – Glen_b Sep 7 '16 at 5:26
• @Glen_b: Thank you. Is this clearer now? – vonjd Sep 7 '16 at 5:41
• It still looks quite close to me. I'll take another look at it in a while. – Glen_b Sep 7 '16 at 5:54
• It looks like your questions are extensively answered at stats.stackexchange.com/questions/26450. Could you identify and highlight any that are not? – whuber Sep 7 '16 at 13:13
• @whuber: I can imagine that there really are good and deep reasons why you should not say that the true mean is within the confidence interval with 95% probability (although I don't see that at the moment) but the problem is that too many people just repeat what they have read without really thinking about it ("it either is or is not within the interval"...). Using the same kind of logic in poker would consequently mean that you would not be allowed to talk about probabilities, nor calculate with them: Either your opponent has a flush or he hasn't. This doesn't make any sense. – vonjd Sep 7 '16 at 15:07