Geometric Distribution Probability
Geometric Distribution Probability
\[P(X=k)=(1-p)^{k-1}p\]
Variables
P = probability of first success on trial k
k = trial number
p = probability of success in one trial
Description
What is this formula?
This formula calculates the probability that the first success occurs exactly on the k-th trial in a sequence of independent Bernoulli trials.
When to use it
Use this formula when repeated independent attempts are performed until the first success occurs.
Example
If the probability of success is 0.2, the formula can estimate the probability that the first successful result appears on the fourth attempt.
Applications
Reliability analysis, telecommunications, quality control, gaming probability, queueing systems, and random event modeling.
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