What Is the Geometric Distribution Calculator?
A geometric distribution calculator models waiting times until the initial occurrence of a Bernoulli event.
How Does the Geometric Distribution Calculator Work?
Multiplies cumulative failure powers by the individual single-trial success rate.
Geometric Distribution Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
P(X = k) = (1 - p)^(k - 1) × p · E(X) = 1 ÷ p
Multiplies probability of (k - 1) consecutive failures by the probability of success on trial k.
How to Use the Geometric Distribution Calculator
- Input your per-trial success probability percentage and your target trial number.
Step-by-Step Example Calculation
20% success rate on trial #3
Input Values:
successProbPct:20
targetTrialK:3
Understanding Your Result
Shows exact probability of first success on trial k, cumulative probability by trial k, and expected average trials.
Factors That Affect the Result
- Per-trial probability directly dictates exponential drop-off rate.
When Should You Use This Calculator?
- Quality control defect screening, oil well drilling success analysis, and gaming drop rate calculations.
Assumptions & Limitations
- Trials must be independent and identical with constant probability.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard discrete probability theory.