The chance of one item being selected out of a set of 3000 is 1/3000. What is the probability of that same item being selected 4 times in 18 time periods?

Question

We are doing data base searches that are supposed to be random, but multiple files are coming up multiple times so we are doing something wrong.

Answer 1

If searches are random and items are allowed to be reselected then you are looking at a binomial distribution with p=1/3000, q=2999/3000, n=18 and r=4.

 

P = ₁₈C₄(1/3000)⁴(2999/3000)¹⁴

 

If you don't want the same item being "selected" then your code needs to "save" the list of items already selected so when an another selection is made the new selection is checked to see if it is already on the list. If it is, it is discarded and a new selection is made until you have the desired number of unique files.