Geometric First Success
Find the chance that the first success occurs on a chosen trial.
Your numbers
First success on trial k
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
Up to three snapshots in this tab. Loading one replaces the current inputs.
Formula
P(T=k)=(1−p)ᵏ⁻¹p; E[T]=1/p
Find the chance that the first success occurs on a chosen trial.
Worked example
- Success probability (%)
- 20
- First successful trial
- 3
- First success on trial k
- 12.8 %
- Expected trials
- 5
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 833db7ee2899 · Example checked: