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Run Rules

This page is designed to give a the exact distribution of the waiting time until the first run of a pre-specified length occurs for the first time, in a sequence of IID Bernoulli trials.

Enter your process parameters:
Probability of success (p): Probability of success in a single Bernoulli trial
Run length (k): The number of successive successes you are waiting for
Longest waiting time: The longest time you are interested in waiting

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Quality is never an accident; it is always the result of high intention, sincere effort, intelligent direction and skillful execution; it represents the wise choice of many alternatives.

— William A. Foster