Poisson: at least one event
Instead of adding every value from 1, use the complement "no event".
Worked example
A server fails on average 0.5 times a month (Poisson). What is P(at least one failure in a month)?
Worked solution
- 1.Complement: P(X ≥ 1) = 1 − P(X = 0)
- 2.= 1 − e^(−0.5) = 0.3935
Typical mistake: Trying to add up every value from 1 instead of using the complement.
Your turn
Three problems of exactly this type, each time with new numbers. Comma or point; fractions like 1/6 work too.
Task
A server fails on average 0.5 times a month (Poisson). What is P(at least one failure in a month)?
P(X ≥ 1) (4 decimal places)
Comma or point; fractions like 1/6 work too.
Formulas for this topic
- P(X = k) = e^(−λ) · λᵏ / k!
- E(X) = Var(X) = λ
- P(X ≥ 1) = 1 − e^(−λ)
Typical mistake: Trying to add up every value from 1 instead of using the complement.
Frequently asked questions
What is the typical mistake in "Poisson: at least one event"?
Trying to add up every value from 1 instead of using the complement.
When do I use Poisson instead of binomial?
For many trials with a very small probability, or when only the average rate λ is known.