The right answer is that with 3 coin tosses, even if all 3 are Heads, the chance of that happening is 12.5% so you cannot reject the hypothesis that the coin is fair at 90% confidence.

With 4 coin tosses, HHHH has a probability of 6.25% which allows you to reject at 90% but not 95%.

With 5 coin tosses, HHHHH has a probability of 3.125% which allows you to reject at 95% but not at 99%.

The point is that, with less than 4 coin tosses you cannot show bias, no matter what. Sometimes you simply don't have enough data to argue statistically.

And statistics can only suggest where to look for actual evidence, it can't prove (or disprove) bias all by itself.

For instance, the contingency table analysis I did yesterday suggests looking for actual (not statistical) evidence of bias in the duration or the trials, not in the result. JakeS posted a theory that indictments were issued in the hopes of gathering sufficient evidence by the time the cases came to trial, which in some cases hasn't happened, resulting in prolongued imprisonments without trial rather than dismissals for lack of evidence. But a theory consistent with statistical suggestions is not evidence.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith

vladimir:

The ideal result should be heads 50% of the time and tails 50% of the time.

You urgently need to go read the first chapter of Feller's An Introduction to Probability Theory and its Applications which covers coin-tossing.

Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith