Geometric Distribution Calculator

Understand the geometric distribution calculator result

The practical job of Geometric Distribution Calculator is modeling repeated independent trials until the first success occurs. It asks for success probability, trial number and reports probability at trial k and cumulative probability. The probability of first success on trial k is one minus p raised to k minus one, multiplied by p. With success probability 0.2, first success on trial three has probability 0.128 and success by then has probability 0.488. By exposing probability at trial k and cumulative probability, Geometric Distribution Calculator makes this specific arithmetic inspectable instead of presenting an unexplained number.

With the page defaults of Success probability 0.2, Trial number 3, the verified output is Probability at trial k 0.128, Cumulative probability 0.488. Trial counting starts at one, so k equal to one represents immediate success. In Geometric Distribution Calculator, each labeled default remains visible while you edit, so you can change one assumption at a time and trace how probability at trial k responds.

Method, limits, and private processing

The model assumes independent trials with the same probability every time. Geometric Distribution Calculator evaluates the entered values entirely in your browser, without sending the inputs to a server. When using its probability at trial k and cumulative probability, retain the stated method and input units because this result is bounded by the assumptions of the probability of first success on trial k is one minus p raised to k minus one, multiplied by p.