I play a guessing game. In this game, there are 100 equally-sized, folded-up cards randomly dispersed in a bag. The cards are labeled 1 through 100. I draw out the cards one by one without replacement and try to guess the number on the card every time I draw. On every guess, I open up the card and see the actual number on it to see if I am correct.
I start by guessing a random number from 1 to 100. I will keep guessing randomly, but I will not guess a number that has already been revealed since that would be silly. How many numbers will I guess correctly?
I wonder if there is a difference between this problem and the problem in which I do not actually get feedback on what specific number I just drew. If there is no difference, then the expected value of correct guesses should be $\sum_{n = 1}^{100} \frac{n^2}{(n + 1)!}$, right?