Binomial Probability Calculator

Binomial probability calculator calculates the probability distribution of the number of successes from a specific occurrence.

Binomial Distribution Formula

The binomial Distribution formula is:
ⁿC_xP^x(1-P)^(n-x)

while
n = number of events.
x = number of successes.
P = Probability of success.
ⁿC_x means combination, it calculates the number of ways to select specific items from total items.
The formula of combination is
n!/(n-x)!x!

Example of Binomial Distribution

For example, if you are on a 20 multi-choice question, that is our number of events (n=20).

Each question has 5 answers, without studying, you have a 20% chance to be corrected for each question, which is 1/5= 0.2.
That is our probability of success (p=0.2).

If you want to get exactly 12 questions right,
that is our number of successes(x=12).

To calculate your probability of 12 questions right, use the formula

n!/(n-x)!x!P^x(1-P)^(n-x)
=20!/(20-12)!12!0.2¹²(1-0.2)^(20-12)
=125970x0.000000004096x0.167772
=0.000086566
=0.00866%

On the other hand, you have over a 99.99% chance that you will get at least 12 questions wrong by guessing the answers.
100%-0.00866%=99.99134%.