To say that a coin is fair you have to toss it a sufficientl large number. Ok!
What is sufficiently? 10.000.000.000 times?
So what if you just finish tossing 10.000.000.000 times and yourcoin give you 10.000.000.000 times head. It could happen!
There is a deep deep contradiction.
What is you toss the coin 10.000.000.000 times and the outcome is 10.000.000.000 times head. Are you going to conclude that the coin is not fair????
What make me suspicious about the probability theory is that at the beginning all started by physical tests.
What is the probability that make some event unlikely to happen?
What is the real meaning of "unlikely" if on the other hand you say that it could happen?
Do not get me wrong. I have a sufficient knowledge of probability theory and maybe deep understanding.
Anyway it is better that we stop the thread.
I`m not native english speaking.
I will have hard time to defend my ideas.
Edit: Written before I saw the suggestion to end the thread.