The Binomial Distribution
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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
Show Probability Table