How to calculate the probability that four specific, distinct numbers from the range 1 - 3000 occur at least once in a fixed sample of 400 random numbers from the range 1-3000? The numbers in the sample can repeat as they were randomly generated.
My intuition would be that it is basically a set of four "scans" of the 400 numbers, so the probability of hitting the 1/3000 searched number in each of the scans is roughly 400/3000 = 2/15. This would give the total probability count as (2/15)x(2/15)x(2/15)x(2/15) = 16/50625 = 0,000316. However, I'm not sure if this accounts (and if it should account) for the fact that it is a fixed sample so it's not "re-rolled" for each of the four scans.
Thanks for any advice.