What is the Geometric Distribution Calculator?

The Geometric Distribution Calculator is a statistical tool that computes the probability of observing the first success on a specific trial in a sequence of independent Bernoulli trials. By entering the probability of success on a single trial and the trial number of interest, the calculator determines the likelihood that the first success occurs exactly on that trial. This is commonly used in quality control, reliability testing, and modeling “first occurrence” events.

How to Use:

1. Enter Probability of Success (p): Input the probability that a single trial is successful. This must be between 0 (exclusive) and 1 (inclusive).
2. Enter Trial Number for First Success (k): Input the trial number where you want the first success to occur. This must be a positive integer (k ≥ 1).
3. Click “Calculate”: The calculator computes the geometric probability using the formula P(X=k)=(1−p)k−1⋅pP(X = k) = (1 – p)^{k-1} \cdot pP(X=k)=(1−p)k−1⋅p.
4. Review Result: The output displays the probability of obtaining the first success exactly on the k-th trial.