# Combination question with and without replacement

There is a group of N unique things. A simple random sample sub group x can be taken without replacement where the number of samples is x, x < N and x = 25% of N. The sample sub group x is replaced after recording. How many simple random samples of size x need to be performed to see 90% of the unique items in group N?

• Sounds like you've got it figured out! To write it properly, one way is to define $Y_i$ as the proportion of the things you've observed up until and including observation $i$. Your recursive function for $E[Y_i]$, the expected number of things you've observed up to observation $i$, would then be $E[Y_i] = E[Y_{i-1}] + 0.25(1- E[Y_{i-1}])$, with the initial condition that $E[Y_0]=0$. – Alton Aug 16 '18 at 22:40