Discrete support uses separate whole-number outcomes; probability is carried by the individual masses.
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Assigning probability to separate outcomes. A discrete probability mass function assigns probability directly to each allowed count or category combination. All mutually exclusive masses across the full support sum to one.
1Define the count support and parameters2Evaluate the requested mass or cumulative range3Check the trial, replacement, and dependence assumptions
Probability mass rule
P(X=k)=C(n,k)p^k(1−p)^(n−k).
A probability mass is a probability at an allowed discrete outcome.
Interpretation and limits
Distribution probabilities are conditional on the entered model and parameters being suitable for the process.
Model boundary: Parameterizations are stated explicitly. A calculated probability does not demonstrate that observed data follow the selected distribution.
Quick guide
How to use this calculator
Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the binomial distribution calculator works
P(X=k)=C(n,k)p^k(1−p)^(n−k).
Distribution probabilities are conditional on the entered model and parameters being suitable for the process.
Worked example
Binomial Distribution example
Exactly 3 successes in 5 independent trials with p=0.5 has probability 0.3125.
P(X=k)=C(n,k)p^k(1−p)^(n−k).
Supported inputs
Precision and limits
Model and design
Parameterizations are stated explicitly. A calculated probability does not demonstrate that observed data follow the selected distribution.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Distribution probabilities are conditional on the entered model and parameters being suitable for the process.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
