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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"?

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closed as off-topic by Zev Chonoles, Gabriel Romon, Robert Cardona, Ali Caglayan, Sujaan Kunalan Mar 17 '15 at 22:03

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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.

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  • $\begingroup$ Thank you. This is precisely what I have been saying all along. $\endgroup$ – KevBelisle Mar 17 '15 at 14:55
  • $\begingroup$ Out of curiosity, your answer holds true even for $N = 33$, $Y = 7$ and $n = 5$, right? $\endgroup$ – KevBelisle Mar 17 '15 at 14:56
  • $\begingroup$ Specify what you mean by "distribution of cards". $\endgroup$ – William Kurdahl Mar 17 '15 at 15:05
  • $\begingroup$ I mean the probability that the next card drawn will be labelled "A". Distribution was probably a poor choice of wording. $\endgroup$ – KevBelisle Mar 17 '15 at 15:08
  • $\begingroup$ Okay, then notice that "the next card" is the same as if you had just picked the sixth card instead of the first card in the beginning. $\endgroup$ – William Kurdahl Mar 17 '15 at 15:10

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