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Geometric Distribution Calculator

Compute the probability of the first success on trial k.

Introduction

Geometric Distribution Calculator — Compute the probability of the first success on trial k. Enter Success probability (p), Trial of first success (k) to get an instant, accurate result.

Formula

PMF (trials until first success): P(X=k) = (1−p)^(k−1) × p, the probability the first success occurs on the k-th trial.

Step-by-step

  1. Enter the Success probability (p).
  2. Enter the Trial of first success (k).
  3. Click Calculate to see your result instantly.

Real-world example

Example: With Success probability (p) = 0.3, Trial of first success (k) = 4, the Geometric Distribution Calculator gives Probability: 0.1029.

Frequently Asked Questions

How is this different from the binomial distribution?
Binomial counts successes in a fixed number of trials; geometric instead counts how many trials are needed to get the first success, with no fixed upper limit on trials.
What is the expected number of trials until success?
The mean of the geometric distribution is 1/p — a lower success probability p means more trials are needed on average.
What inputs does the Geometric Distribution Calculator need?
You'll need to provide: Success probability (p), Trial of first success (k). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Geometric Distribution Calculator?
The Geometric Distribution Calculator applies the formula exactly as calculated — PMF (trials until first success): P(X=k) = (1−p)^(k−1) × p, the probability the first success occurs on the k-th trial. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Geometric Distribution Calculator free to use?
Yes, the Geometric Distribution Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Geometric Distribution Calculator

The Geometric Distribution Calculator uses a real, verifiable formula — PMF (trials until first success): P(X=k) = (1−p)^(k−1) × p, the probability the first success occurs on the k-th trial. — so results are accurate every time, not an approximation.