Geometric First-Success Probability Calculator
Geometric First-Success Probability is intended for the specific statistics task described by its name. Enter success probability per trial, trial number of first success to calculate a result expressed in %. The formula works entirely in your browser and needs no account or external API. Assumes independent identical trials. This estimate is useful for comparing scenarios when the supplied measurements follow the stated assumptions.
How to use this calculator
- Measure success probability per trial in the units indicated on the input label.
- Enter Trial number of first success.
- Read the % result, then compare alternative inputs to evaluate your own situation.
Geometric First-Success Probability formula
100*Math.pow(1-p,n-1)*p (%).
- The expression 100*Math.pow(1-p,n-1)*p combines Success probability per trial, Trial number of first success. Follow the units on each input: the answer is expressed in %.
- Assumes independent identical trials.
Worked examples
Worked example: Geometric First-Success Probability
Use these sample measurements: Success probability per trial = 0.2, Trial number of first success = 4.
Compute 100*Math.pow(1-p,n-1)*p.
Using the example inputs, the result is 10.24 %. Use this value to verify the formula before changing the measurements.
Understanding the result
Interpret the output as %; it is not a measurement taken directly from a physical system.
Assumes independent identical trials.
Important notes
Assumes independent identical trials.
Review the input units, any required legal or engineering rules, and unusual edge cases before acting on this estimate.
Frequently asked questions
What does Geometric First-Success Probability calculate?
It evaluates 100*Math.pow(1-p,n-1)*p to produce % from the measurements you enter. For the example values shown, the result is 10.24 %.
Which assumptions matter most?
Assumes independent identical trials.
Can I compare two scenarios?
Yes. Enter another set of measurements in the same units and compare the two outputs.
Related calculators
- Percentage Calculator — Calculate percentages, percentage of a number, and percentage change between two values.
- Number Base Converter — Convert numbers between binary, decimal, hexadecimal, and octal.
- Fraction Calculator — Add, subtract, multiply, and divide fractions with step-by-step simplification.
- LCM & GCD Calculator — Find the Least Common Multiple and Greatest Common Divisor of any set of numbers.
- Roman Numeral Converter — Convert numbers to Roman numerals and Roman numerals back to numbers.
- Prime Number Checker — Check if a number is prime, and find all prime numbers up to any limit.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Probability — Learn basic probability formulas, complementary probability, and how to calculate simple event chances.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Probability — Understand probability as a measure of how likely an event is and review simple probability formulas.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.