Geometric Distribution

The geometric distribution is a probability distribution that models the number of trials needed to get the first success in a sequence of independent Bernoulli trials. In other words, it describes the number of failures before the first success occurs.

$P(X = k) = (1 - p)^{k-1} \cdot p$

• $X$ is the random variable representing the number of trials until the first success
• $k$ is the number of failures before the first success ($k = 1, 2, 3, \ldots$)
• $p$ is the probability of success in each trial ($0 \ge p \ge 1$)

Probability of success in each trial with probability of 0.5.