I have a homework assignment on probability that goes like this:
Two cards are selected one after the other, at random and without replacement, from a well-shuffled, standard deck of 52 playing cards. Let A1 be the event that the first card selected is an ace, and let A2 be the event that the second card selected is an ace. What is the probability that the second card selected is an ace?
The solution argues that because we don't know what we picked first, the probability that the second card selected is an ace is still $\frac{4}{52}$. However, I am very confused by the idea that not knowing what was picked, is equivalent to assume that an ace was not picked.
Also, this leads to the following sort of paradox. Given two observers, one who knows what is on the first card, the other who does not, the probability of picking an ace on the second card changes from conditional to unconditional.
Instead, I would see the experiment as a case of conditional probability in both cases, which cannot be estimated unless we know what is on the first card.