The **geometric distribution** is a discrete probability distribution -- the probability distribution of the number of Bernoulli trials needed to get one success, if the probability of success is *p*. The probability that the first success is on the *n*th trial is:

for *n* = 1, 2, 3, ....

The expected value of a geometrically distributed random variable is 1/*p* and the variance is (1 − *p*)/*p*^{2}.

It is the special case of the negative binomial distribution in which *r* = 1. Like its continuous analogue (the exponential distribution), the geometric distribution is "memoryless"; in fact, it is the only memoryless discrete distribution.

See also negative binomial distribution.