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.

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