Poisson Probability: λ = 3, k = 3 Events
The probability of exactly 3 events when λ = 3 (the mean equals the observed count) is approximately 22.4%.
How to use this tool
- Enter rate (λ) and events (k) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your p(x = k) and the full breakdown beneath it.
Calculate the Poisson probability when the number of observed events equals the average rate—a common textbook scenario.
Frequently asked questions
- When should I use the Poisson distribution?
- Use Poisson when counting events in a fixed interval of time or space, where events occur independently at a known average rate λ. Examples: emails per hour, accidents per week, typos per page.