Does discarding cards face down affect the distribution of the remaining cards?

Question

You have a deck of $N$ cards, $Y$ of which are labelled "A". $N$ and $Y$ are known.

Does discarding $n$ cards face down from the top of the deck affect the probability that the next card drawn is labelled "A"?

Answer 1

Let's say you have $N=$3 cards, with $Y=2$ being labelled "A". You then discard $n=$2 cars. Now the last card has $67$% chance of being labelled "A", but the remaining set of 1 cards cannot contain 2 cards with "A" on it.

So the $67$% remains the same while the distribution of number of "A" cards changes.