Let $ n ∈ N $. Two packs of cards each containing cards numbered 1 to $ n $ are shuffled and placed on the table. One by one, two cards are simultaneously turned over from the top of the packs. What is the probability that at some point the two revealed cards have the same number?

Could anyone write a detailed solution explaining each step? I would be really thankful.( I know there is a similar question to this but it does not help me in any way)

  • $\begingroup$ You want the probability that one pack is not a derangement of the other. $\endgroup$ – N. F. Taussig Apr 9 at 16:18
  • $\begingroup$ @N.F.Taussig Yes, I've seen your comment on the other question but I do not know how to calculate this probability. Also, I have still not studied dearangements in combinatorics, but I am open to incorporate it but I'd need an explanation of the Probability though $\endgroup$ – The Poor Jew Apr 9 at 16:32

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