Calculate the probability of observing exactly k events when the mean rate is λ.
| P(X = k) | – |
Use this calculator for counts of rare or random events in a fixed interval of time or space, such as calls per hour, defects per batch, or arrivals at a counter, when events occur independently at a constant average rate λ.
The formula is: P(X = k) = e^{−λ} λ^k / k!. Enter λ as the expected count in the same interval you care about, and k as a whole number of events. For λ = 3 and k = 2, P(X = 2) ≈ 0.2240.
The Poisson model assumes independent events and a stable rate. It is a probability of exactly k events, not at least k. Very large k can overflow a factorial; keep k within ordinary count ranges.
Mean rate (λ): Expected number of events in the interval.
Events (k): Count whose probability you want, an integer of at least 0.
P(X = k): Probability of exactly k events.
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