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Concept

Geometric Distribution

The geometric distribution is the probability distribution that describes the number of binomial trials needed in an experiment until the first success occurs. The trials must satisfy three conditions.
  1. There are two possible outcomes for each trial — success and failure.
  2. The trials are independent.
  3. The probability of success is the same on each trial.

If is the probability of success and is the number of trials needed to get a success, the probability of getting a success in trials is given by the formula below.

Example

Consider a situation that a regular coin is flipped until it lands on heads.
Coin Flip
It is worth noting that this experiment satisfies the three conditions for a geometric distribution.
  1. There are two possible outcomes — heads or tails.
  2. Each trial is independent.
  3. The probability of landing on heads is for every trial.
The following expression gives the probability of landing heads on trials.
The graph below displays the probabilities for values of from to The value of indicates that the coin is flipped once before it lands on heads. The value of indicates that the coin lands on head the second time it is flipped, and so on.

It should be noted that the probability of landing heads on coin flips is equal to the probability of landing tails on consecutive coin flips, then landing heads on the next flip.