Players A and B each have a well shuffled standard pack of cards, with no jokers. The players deal their cards one at a time, from the top of the deck, checking for an exact match. Player A wins if, once the packs are fully dealt, no matches are found. Player B wins if at least one match occurs. What is the probability that player A wins?

Question

Players A and B each have a well shuffled standard pack of cards, with no jokers.  The players deal their cards one at a time, from the top of the deck, checking for an exact match.  Player A wins if, once the packs are fully dealt, no matches are found.  Player B wins if at least one match occurs.  What is the probability that player A wins?

zarkon · Answer

use Inclusion-Exclusion Principle