Binomial Probability Calculator

Number of Successes: (integer; >=0)
Number of Trials: (integer; >=1)
Probability of Success: (between 0 and 1)
      
Exact Probability:
Cumulative Probability:

Binomial Probability Definition

The Binomial distribution is used for outcome variables with two exclusive categories, such as "Yes" and "No", "Success" and "Failure". One common example is the coin toss, with two exclusive outcomes of "head" and "tail".

Binomial Probability Example

For a fair coin toss, the probability of getting a head or a tail is each at 0.5. If we toss a fair coin 10 times, the "exact probability" that we get EXACTLY 4 heads is at 0.205078125; and the "cumulative probability" that we get NO MORE THAN 4 heads (0 heads, or 1 head, or 2 heads, or 3 heads or 4 heads) is at 0.376953125.

In Microsoft Excel, BINOM.DIST(4,10,0.5,0)=0.205078125; BINOM.DIST(4,10,0.5,1)=0.376953125

Similarly in TI83/TI84, binompdf(10,0.5,4)=0.205078125; binomcdf(10,0.5,4)=0.376953125