I'm having a rough time finding 4 different probabilities. Say you have a deck of only 4 different cards, you draw one card, put it back in the deck & shuffle it. You continue drawing one card, put it back & shuffle the deck until you draw one card you've seen before.
I want to find the probabilities of the cycle ending at the 2nd, 3rd, 4th & 5th draw.
I realize that you will draw at least 2 cards out of the deck before ending the cycle, in the case of drawing the same card both times. And if you get to the 5th card the cycle will end because that means you've drawn all 4 different cards once.