So I have in excel the numbers of 0 to 36. Following the poisson distribution [POISSON.DIST(0,18,,FALSE)], i found the probability of each number to come out. The computer generates a random number between 0 and 1 and then it looks up that number in the range of intervals and tells me what number was for example 4, 18, 35 or any number between 0 and 36. Is there a way to find the minimum amount of times a random number is generated in order that all numbers have come out at least once?
2026-04-01 10:24:57.1775039097
How can I find the minimun amount of 'spins' so all numbers have come out at least once?
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Given a truly random process, there is no minimum. You can make the probability of generating all numbers as close to $1$ as you like by generating enough numbers, but you cannot make it equal $1$.
For Excel, the minimum number of tries before you generate every number is a function of exactly what pseudorandom process it uses to generate the "random" values between $0$ and $1$. But that's a number-theory question, not probability, and it requires explicit knowledge of the algorithm used by Excel.
Also, a true Poisson distribution has no upper bound on the possible outcomes. It should be possible that it will sometimes generate a number greater than $36$.