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?
This sounds like a homework question, so I'm a bit weary of providing the answer, but maybe I can help you think about it.
I'm going to assume you're looking for the expected number of samples to exceed 90% of observation.
After sample 1 you will have observed 25% of the things. In sample 2, the probability of observing any individual thing is 0.25, so the expected number of new observations you will make is the proportion of items you haven't yet observed times the probability that each is observed. Using this you should be able to set up a recursive function to calculate the expected proportion observed after each sample.
Also, I suggest changing how you tagged this question, because this is not statistics, it's probability.