# Binomial Distribution Calculator

This is used to calculate coin toss probabilities.

 Enter probability of heads p = 0 < p < 1 Enter number of tosses n =

## Probability of exactly k heads

 b(k) = $$\binom{n}{k}p^k(1-p)^{n-k}$$ Binomial Distribution b() Normal approx:

## Probability of k or less heads

 F(k) = $$\sum_{i=0}^{k}b(i)$$ Cumulative Distribution F() Normal approx:

## Probability of more than k heads

 1 - F(k) = $$\sum_{i=k+1}^{n}b(i)$$ 1 - F() Normal approx:

See our book The Coin Toss: The Hydrogen Atom of Probability to learn about coin toss statistics.