A jar holds 3 white and 2 black counters. They are drawn out one at a time at random, without replacement, until the jar is empty. What is the probability that the LAST counter drawn is white?

Think of the five counters being laid out in a random order. Each of the 5 positions is equally likely to hold any particular counter, so the last position is white with probability 3/5 — exactly the same as the first draw. No long case-by-case calculation is needed, and the answer would be the same for any position you asked about.