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There are 3 decks each of ten cards, and you are playing a game with your friend. You got a bonus which allows you to look through your friends cards. Your friend then shuffles their cards and you pick the one on top. Suppose you want a particular card, and your friend has x number of cards, what's the probability that they have the card you want and after the shuffle you get it?

So, I reasoned that the probability that they have the card I want is x/30. And the probability that I get it from them is 1/x. I reasoned that them having the card and me getting the card is an and case, so would the probability be 1/x*x/30 = 1/30?

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  • $\begingroup$ Are the cards in the decks the same, so there are three copies each of ten different cards? Otherwise, why refer to three decks of ten instead of one deck of thirty? $\endgroup$ Commented Nov 24, 2019 at 21:33
  • $\begingroup$ Each deck is of a different color. So there are three of the same value but of different colors. $\endgroup$ Commented Nov 24, 2019 at 22:05

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You are correct here, though the problem wording is rather strange.

You could think about it this way: the intermediate step of your friend picking X cards and you looking at them has no effect on the result, so it is the same probability as picking one card out of 30.

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