Match Made in Heaven
A solitaire type of card game is played as follows: The player has two shuffled decks, each with the usual 52 cards. With the decks face down the player turns up a pair of cards, one from each deck.
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If they are matching cards (for example, if both are the seven of spades) he has lost the game.
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If they are not matching cards he continues and turns up another pair of cards, one from each deck.
Again he has lost if they are a matching pair. The player wins if he can turn up all 52 pairs, none matching. What is the probability of a win?
Give your answer to 3 decimal places.
The answer is 0.3679.
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1 solution
The answer is 1 - P(loss). P(loss) would come from the Union-Intersection law as 52C1 ×1/52 - 52C2×1/52*51 + 52C3........ , which would reduce to 1 - 1/2! + 1/3! - 1/4!.....- 1/52! ~ 0.63. Thus, 1 - P(loss) = 0.37