The geometric distribution is somewhat similar to the binomial distribution. It's a probability distribution with a particular setting; it has a geometric setting.
A scenario or an experiment can be considered geometric if it fits the following four criteria:
You can liken this to the lottery because you're only going to play until you win. You essentially play and lose all the way up until you win, and then you stop.
EXAMPLE
Suppose a soda company is running a promotion called Lucky 7, where people can win free bottles of soda by looking under the cap. They advertise one in seven wins, and what they mean is that one out of every seven bottles has caps that say "winner" on them.You can actually come up with a formula here to find the probability for the first success in a trial.
If the geometric distribution is appropriate and x is the number of trials until you get a success, then the probability that it takes you exactly k trials to obtain a success probability of success is p. You only do that once.
You fail every time except for the last time when you succeed.
Source: Adapted from Sophia tutorial by Jonathan Osters.