Geometric Probability Calculator
Calculate probability of first success on nth trial
About this calculator
The Geometric Probability Calculator determines the likelihood of achieving the first success on a specific trial number in a sequence of independent Bernoulli trials. This calculator is essential for statisticians, researchers, and students analyzing scenarios like quality control testing, survey responses, or any situation where you need to find the probability of the first positive outcome occurring on the nth attempt. It's particularly useful in reliability engineering and risk assessment applications.
How to use
Enter the probability of success for a single trial (between 0 and 1) and specify which trial number you want to analyze. The calculator will compute the geometric probability using the formula P(X=n) = (1-p)^(n-1) × p, where p is the success probability and n is the trial number.
Frequently asked questions
What is geometric probability used for?
Geometric probability models scenarios where you're waiting for the first success in repeated independent trials, like quality testing or medical diagnoses.
How is geometric probability different from binomial?
Geometric probability focuses on the trial number of the first success, while binomial probability counts total successes in fixed trials.
What are the requirements for geometric distribution?
Trials must be independent, have constant success probability, and continue until the first success occurs with only two possible outcomes.