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How to Calculate Poisson Probability

What is Poisson Probability?

Poisson distribution models the number of events in a fixed interval when events occur independently at a constant average rate. Used for rare event probability.

Formula

P(X = k) = (λᵏ × e⁻λ) / k! where λ is the average rate

Step-by-Step Guide

  1. 1Enter λ (average number of events)
  2. 2Enter k (number of events of interest)
  3. 3Calculate using the Poisson formula

Worked Examples

Input
λ = 3, k = 2
Result
P(X = 2) ≈ 0.224
(3² × e⁻³) / 2! ≈ 0.224

Common Mistakes to Avoid

  • Confusing λ with the event value
  • Using Poisson when binomial is more appropriate

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