Geometric Probability Calculator
Calculate geometric probability online. Find the probability of first success on a specific trial with our easy-to-use Geometric Probability Calculator.
Geometric Probability Inputs
Enter the probability of success on a single trial (p) and the desired number of trials until the first success (k).
Result
Probability of first success on trial :
Probability Visualization
Understanding Geometric Probability
Geometric probability deals with the number of trials needed to get the first success in a sequence of independent Bernoulli trials. A Bernoulli trial is an experiment with only two outcomes: success or failure.
Formula
- P(X=k) is the probability that the first success occurs on the k-th trial.
- p is the probability of success on each trial.
- k is the number of trials until the first success (k = 1, 2, 3, ...).
Example
Suppose you are rolling a fair die until you get a 6. The probability of success (rolling a 6) is 1/6. What is the probability that the first 6 appears on the 3rd roll?
- Probability of success (p) = 1/6
- Number of trials until first success (k) = 3
- Using the formula: P(X=3) = (1 - 1/6)^(3-1) * (1/6) = (5/6)^2 * (1/6) ≈ 0.1157
This calculator helps you quickly compute this probability for different values of p and k.