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?