Discussion:
Q: Suppose we turn over cards simultaneously from two well shuffled decks of ordinary playing cards. We say we obtain an exact match on a particular turn if the same card appears from each deck: for example, the queen of spades against the queen of spades. Let pm equal the probability of at least one exact match.
Show that:
pm= 1-(1/2!)+ (1/3!) - (1/4!) +... - (1/52!).