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Geometric Distribution — result sheet
Calculate the probability that the first success occurs on a selected trial and the cumulative probability by that trial.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(X=k) = (1-p)^(k-1) p; P(X<=k) = 1 - (1-p)^k.
The geometric distribution models the trial count until the first success in independent Bernoulli trials with a constant success probability. The tool reports both an exact-trial probability and a by-that-trial cumulative probability.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Success probability p — minimum 1.0E-9; maximum 1
- Trial of first success k — minimum 1; maximum 100000
Worked example
| Input | Value |
|---|---|
| Success probability p | 0.2 |
| Trial of first success k | 3 |
P(X=3)=0.128; P(X<=3)=0.488.
Assumptions and limits
- Trials are independent and have the same success probability p.
- X counts trials, so the first possible success is k=1.
- The model does not infer dependence, changing odds, stopping rules, or a real-world cause for success.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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