I need to find a probability, that from 400 observations there will be more than 30 and less than 50 successful events. Probability, that event will succeed is 0.1. Events are not influencing each other and success probability is constant.

I have tried to use a puason formula for that, summing up all the probabilities, but result was way over the probabilities maximum. Example - Example

This was the equation for the part - from 30 to 50. Part to 30 was almost the same, but without the first summation.


1 Answer 1


Instead of using Poisson distribution, use Binomial distribution with parameters $n=400$ and $p=0.1$. The desired probability is $$ P(30<X< 50)=\sum_{k=31}^{49}\dbinom{400}{k}(0.1)^k(0.9)^{400-k} $$

Note: using Poisson distribution is an approximation to your problem since $n$ is big and $p$ is small. The parameter will be $\lambda = np = 40$ and the desired probability $$ P(30<X< 50) = \sum_{k=31}^{49}\dfrac{e^{-40}(40)^k}{k!}. $$


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .