Things on this page are fragmentary and immature notes/thoughts of the author. Please read with your own judgement!
https://projecteuler.net/problem=436
\(X_i \sim Bernoulli(p)\)
$$\bar{X}_n \dot{\sim} N(p, \frac{p(1-p)}{n})$$
$$[\bar{X}\pm C_{\alpha} \sqrt{\frac{p(1-p)}{n}}]$$
$$\frac{c_{\alpha}}{\sqrt{n}} \le 0.5\times 10^{-10}$$
$$n \ge 10^{20} C_{\alpha}^2$$