Flipping coins- percentages of heads vs tails If I flip a coin multiple times and count the number of time it fell on heads and the number of times it fell on tails and keep a track of them. In how many flips on average will the delta between percentage of heads and percentage of tails will be less than 0.1%?


I want to check if a coin is fair(lands 50% of the times on each
  side. I assume that delta of 0.1% between them is fair). How many
  flips do i need in order to be 99% confident that the coin is fair?

For large n you can apply moivre laplace. So you approximate the binomial distribution by the normal distribution. 
Let $p=\frac{X}{n}$, where $X\sim Bin(n,0.5)$. The equation becomes
$P(|\frac{X}n-0.5|\leq 0.001)=2\Phi\left(\frac{0.001}{ \frac{0.25}{\sqrt n}} \right)-1=0.99$
$\Phi\left(\frac{0.001}{ \frac{0.25}{\sqrt n}} \right)=0.995$
$\frac{0.001}{ \frac{0.25}{\sqrt n}} =\Phi^{-1}\left(0.995\right)$
$\frac{0.001}{ \frac{0.25}{\sqrt n}} =2.576$
$\sqrt n=2.576\cdot \frac{0.25}{0.001}$
$n=414,736$
