Binomial Distribution Calculator

Number of Trials (n) =

Number of Successes (x) =

Probability of Success (p) =

Probability of Failure (q) =



Binommial Distribution Formula

P(x) = (n! / (n - x)!x!)pxqn-x

n: The number of trials

x: The number of successes

p: The probability of success

q: The probability of failure (which is 1 - p)

The binomial distribution  describes the behavior of a count of variable X if the following conditions apply:

1- The number of observations n is fixed.
2- Each observation is independent.
3- Each observation represents one of two outcomes ("success" or "failure").
4- The probability of "success" p is the same for each outcome.

Sample Binomial Distribution Problem

Alex has a nickel and he is going to flip it 3 times, what is the probability of the coin flips resulting in 2 heads?

Below is the possible results:

To solve for this problem using the formula, it will look like the following:
n: 3 (3 flips)
x: 2 (there are only two alternatives, heads or tails)
p: .5 (there is a 50% probability of getting heads)
q: .5 (there is a 50% probability of getting tails)

P(2 heads) =
(3! / (3 - 2)!2!).52.53-2

The answer to this problem is .375, which means there is a 37.5% probability of 2 heads occuring out of 3 flips.

Additional Pagess

Standard Deviation Insights

StandardDeviationCalculator.net - We offer an easy to use standard deviation calculator with the standard deviation formula, examples, explanation and other related information. Our site is for students, business professionals, or just for personal use. Input is always welcome (no pun intended!), contact us and we will review your suggestions.
Thank you for visiting our site.