Paritian

Statistics

Binomial Probability Calculator

Probability of exactly k successes in n independent trials, with the expected value.

Results

Probability 0.11718750
Percentage 11.71875 %
Mean (average) 5.0000
Standard deviation 1.58114
How it changes
ProbabilityNumber of successes 0 – 10. Probability: 0.10 → 0.10Probability0.005.0010.0015.0020.0025.000246810Number of successes

The dashed line marks the value you entered.

What this tool does

This answers questions of the shape “what are the chances of exactly three heads in ten tosses”, and the same shape covers defect counts, survey responses and pass rates. The trials must be independent and each must have the same probability of success.

Formula

P = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ

Variables

SymbolMeaningUnit
nNumber of trials—
kNumber of successes—
pProbability of one success—
PRProbability—
PCPercentage%
EXMean (average)—
SDStandard deviation—

Worked example

  • Number of trials10
  • Number of successes3
  • Probability of one success0.5
  • Probability0.11718750
  • Percentage11.71875 %
  • Mean (average)5.0000
  • Standard deviation1.58114

Limitations

  • The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.