3 ms·
I guess another way of stating the problem is this: say you toss a coin and get heads the first 1000 times. Now you are likely to believe that the coin is biase
by prmph 10y ago
I guess another way of stating the problem is this: say you toss a coin and get heads the first 1000 times. Now you are likely to believe that the coin is biased. But that cannot be proved. It may be that you have simply not tossed the coin enough times to perceive its fairness. Maybe after the 1000th toss you start to get enough tails such that after the millionth toss, it is not at all clear that there is any bias.
So practically we can make a judgement as to whether the coin is biased on not based on how many tosses we think is sufficient, but theoretically it is impossible to distinguish a biased coin from a fair one if we toss to infinity
- danbruc 10y agoYes, that is exactly what I had in mind. Probabilities are weired in the way that they say what will happen but then still leave open the possibility that this will not happen at all. You toss a coin a billion times, you will get about 500 million heads. Well, or you don't and there are exactly zero heads.
- srean 10y ago> theoretically it is impossible to distinguish a biased coin from a fair one if we toss to infinity correction: if you replace infinity by any large finite number your statement is correct.