The Geometric distribution counts trials until the first success: memoryless waiting, a planning quantile, and how it bridges to Exponential and Negative Binomial.

The Exponential distribution models constant-rate waiting times: density is not probability, the survival and hazard functions, memorylessness, and when it fails.

The Poisson distribution counts constant-rate events in an interval: separating rate from expected count, the mean-equals-variance diagnostic, and the bridge to Exponential.

The Binomial distribution counts successes in a fixed number of independent, equal-probability trials: model card, shape, a worked at-least calculation, and when it fails.

A map of ten common probability distributions organized by the random process each one describes, with a pick-a-distribution selector table.