"Two shuffled decks are laid out one beneath another...what is the expected number of matches" (match is same rank and suit)
Part where i am stuck-
Does the probability at each draw for a match stays same equal to $\frac{1}{52}$. Shouldnt the probability of a match on the second draw be $\frac{1}{51}$ if there was a match on the first draw
and $\frac{1}{50}$ if there wasn't a match on the first draw
How does one go from here to computing the expected value?
Edit: Looking to understand why Expected value at ith draw is always same at $\frac{1}{52}$...to me it looks like the probability at ith draw would depend on previous draws.