Geometric Distribution Calculator

The geometric distribution answers a simple but important question: if you repeat an experiment with a fixed probability of success on each attempt, what is the chance that your first success comes on exactly the k-th try? Each attempt is independent and has the same probability p of succeeding. A free-throw shooter with a 30 percent success rate, a quality control inspector checking items until finding the first defect, or a student re-sitting a test until they pass: all of these follow the geometric distribution. The probability that the first success occurs on trial k is P(X = k) = (1 minus p) to the power (k minus 1) times p. The cumulative probability P(X less than or equal to k) = 1 minus (1 minus p) to the power k gives the chance of succeeding by trial k. The expected number of trials to first success is 1 divided by p. This calculator takes the success probability p (between 0 and 1) and the trial number k (a positive integer), and returns the exact probability P(X = k), the cumulative probability P(X less than or equal to k), the probability of still waiting P(X greater than k), and the distribution mean, variance and standard deviation. It is useful for students studying probability theory, quality engineers, sports analysts and anyone dealing with repeated Bernoulli trials.

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P(X = k) = (1-p)^(k-1) times p. P(X ≤ k) = 1 - (1-p)^k. p must be between 0 and 1 exclusive. k must be a positive integer.