The binomial distribution gives probabilities for the number of successes observed in n Bernoulli trials, each
with success probability p.Change the values of n and p to see how the shape of the distribution changes.

Number of Bernoulli Trials (n):

Probability of Success (p):

Number of Bernoulli Trials (n):

Probability of Success (p):

Enter Numbers for n and p

Overlay Normal Distribution

Hover over a bar in the graph to see the probability for the corresponding number of successes, or consult the table below.

Probability Table:

Number of Bernoulli Trials (n):

Probability of Success (p):

Type of Probability:

Value of x:

Value of x_{1}:

Value of x_{2}:

Show Probability Table

Overlay Normal Distribution

Formulas for the distribution function $P(X = x)$ and the cumulative distribution function $P(X \le x)$ are shown to the right.

The distribution function $P(X=x)$ finds the probability of observing exactly $x$ successes in $n$ Bernoulli trials, each with success probability $p$.

The cumulative distribution function $P(X \le x)$ gives the probability of observing $x$ successes or fewer.

Number of Bernoulli Trials (n):

Probability of Success (p):

Number of Success (x):

For calculations with values of n or p not selectable via the sliders, please go to the Find Probability tab, where you can enter any values for n and p.

Probability Table:

Number of Bernoulli Trials (n):

Probability of Success (p):

Guaranteed Percentage in Lower Tail (in %):

Note: The actual percentage in the lower tail may be considerably higher, but the quantile computed is the smallest possible with the guaranteed percentage in the lower tail