Binomial & Poisson Probability Calculator
Binomial & Poisson Probability Calculator: Computes Binomial PMF: C(10, 2) * 0.5^2 * 0.5^8 and Poisson PMF: (2^2 * e^-2) / 2!.
About this binomial & poisson probability calculator
Binomial & Poisson Probability Calculator — browser-based utility.
How this tool works
Calculation and parameter relationship: binomial=C(trials,k)×pᵏ×(1−p)^(trials−k); poisson=exp(−lambda)×lambdaᵏ/k!
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Worked example
Scenario: Compare the probability mass for exactly two successes under supplied binomial and Poisson parameters.
Sample input:
Processing: Require 0 ≤ k ≤ trials, 0 ≤ p ≤ 1 and lambda ≥ 0; calculate C(n,k)p^k(1−p)^(n−k) and exp(−lambda)lambda^k/k!.
Illustrative output:
Limits and verification
Parameter domains and units: k,trials ∈ ℤ; 0 ≤ k ≤ trials ≤ 170; p ∈ [0,1]; lambda ≥ 0; PMF ≠ CDF; binary64. Results use binary64 floating-point numbers unless BigInt is stated. Result cards show up to 10 significant digits; raw output retains the serialized value. A null ratio means the model has no meaningful finite value for that ratio; it is not zero.
Examples demonstrate an expected workflow; they do not prove every input or every branch of an external specification. Check important results with an independent source before using them for money, security, compliance, safety, or irreversible file changes.
Browser processing boundary
Tool input is processed by code running in the browser and is not intentionally sent to a CZOA processing API. The page can still request ordinary site assets, analytics, or advertising when those services are enabled. Browser extensions and managed-device software remain outside this tool's control.
Relevant references
These references govern or help explain the format, protocol, or calculation used here. Listing a reference does not claim certification or complete implementation of every optional feature.
Content owner: CZOA Tools · Last reviewed: 2026-09-15 · Review methodology
How to use it
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Frequently asked questions
How are the two probabilities calculated?+
The tool computes the binomial mass C(trials,k) × p^k × (1−p)^(trials−k) and the Poisson mass exp(−lambda) × lambda^k / k!. Both results use the same integer k, but describe two separate distributions.
What can I enter in the calculator?+
The interactive workspace provides fields for k, trials, p, and lambda, and Raw JSON / Advanced accepts {"k":2,"trials":10,"p":0.5,"lambda":2}. Run locally after entering all four fields.
Which input boundaries and precision limits apply?+
k and trials must be integers with 0 ≤ k ≤ trials; p must be from 0 to 1 and lambda must be nonnegative. Outputs use JavaScript binary64 arithmetic, so they are probability masses rather than cumulative probabilities or a fitted distribution.
What did the isolated browser calculation return?+
For {"k":2,"trials":10,"p":0.5,"lambda":2}, the isolated browser returned binomial 0.0439453125 and poisson 0.2706705664732254. This confirms the tested local PMF calculation only, not cumulative probabilities, fitted distributions, or statistical conclusions.