Re:Make a Fair Coin from a Biased Coin (2018)
by mannerheim on Wednesday March 16, 2022 @03:51AM
(#30696323)
To be fair, a 1% bias would probably not be detected in a hundred trials. CI for Bernoulli is +/- z * sqrt(p * (1-p) / n), so for a 95% confidence interval smaller than a percentage point, we have
1.96 * sqrt(p * (1-p) / n) = 0.01
0.5^2 / n = (0.01/1.96)^2
n = (1.96/0.01 * 0.5)^2
Or about 9604. So you need roughly 10k trials to determine with 95% confidence a bias of 1%.
1.96 * sqrt(p * (1-p) / n) = 0.01
0.5^2 / n = (0.01/1.96)^2
n = (1.96/0.01 * 0.5)^2
Or about 9604. So you need roughly 10k trials to determine with 95% confidence a bias of 1%.