This is from a practice exam where I know the answer, but can't seem to prove it for all cases.
Problem: Suppose you have an urn filled with M objects, W are white. What is the probability that if you select n objects without replacement the ith will be white.
My thoughts: If you do the expansion out for 2 objects, you see that the probability of the second choice being white works out to W/M, as though the first choice didn't matter.
I can't seem to come up with an argument either using conditional probability or independence that would explain that all choices from the urn from the 1st to the ith-1 don't matter. However since we're picking without replacement, they seem like they should matter when we make our ith pick?