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Probability of repeated events

Independent trials: at least one success, no successes, and expected counts.

Showing a worked example. Change the values and the result updates, and the answer lives in the URL.

Over 20 independent trials

Probability of one event5%
Odds of one event1 in 20
No occurrences35.84859224%(1 − p)ⁿ
At least one occurrence64.15140776%1 − (1 − p)ⁿ
Expected number of occurrences1np
Standard deviation0.974679√(np(1−p))
Trials for a 50% chance13.5134
Trials for a 95% chance58.404

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Probability of repeated events | Nerdulator