Coin Flip Probability Calculator

Coin flip probability calculator calculates the probability of heads or tails that occur during specific coin flips.

Coin Flip Probability Formula

The coin flip probability formula is :
P=n!/(n-x)!x!2ⁿ
while
n = coin flip times.
x = heads occurs times.

It is derive from the binomial Distribution formula:
n!/(n-x)!x!P^x(1-P)^(n-x)

while
n = number of events.
x = number of successes.
P = Probability of success.

In the coin flip probability formula,
n!/(n-x)!x! is to calculate the combination of head or tail that occurs.

2ⁿ is to calculate the total possible combination of coin flips,
since there are 2 sides to the coin, each flip will have 2 choices, either head or tail.

For example, if the coin is flipped 5 times, the total possible combination is
2⁵=32.

Last, divide the combination of heads that occurs by the total possible combination, that is our probability.

Coin Flip Probability Example

For example, to calculate the probability of exactly 3 heads from 10 coin flips.
First, we calculate
10!/(10-3)!3!
=120

And then 10 flips will have
2¹⁰
=1024 combination.

Therefore, to have 3 heads of 10 coin flips, the probability is
1201024=11.72%