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8 decks of playing cards are used in baccarat initially. In each game 4 cards are drawn from the shoe which contains the 8 decks of cards (416 cards in total), in which 2 cards for Banker and 2 cards for Player. What is the probability of having at least one pair in a Baccarat game (that is, either Banker or Player get a pair or both got a pair)?

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closed as off-topic by Behaviour, Daniel Rust, Hakim, dragon, Paul Jul 4 at 1:11

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Please give your solution. –  Ram Feb 1 '13 at 11:08

1 Answer 1

Hints:

  • Find the probability that the second card drawn is the same as the first
  • Double that (either the player of the banker may have a pair)
  • Reduce the result as both may have a pair, which will have been counted twice
    • subtract the probability they have the same pair
    • subtract the probability they have different pairs pair
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