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 Two Packs Of Cards (Posted on 2004-02-05)
Two identical pack of cards A and B are shuffled throughly. One card is picked from A and shuffled with B. The top card from pack A is turned up.
If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?

 See The Solution Submitted by Ravi Raja Rating: 3.8571 (7 votes)

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 re: Solution | Comment 2 of 14 |
(In reply to Solution by stan)

Given that the Queen of Hearts was turned up on the first deck, the card that was transferred to deck B is equally likely to be any one of the 51 other cards in the deck, so the probability is

(1/51)*(2/53)+(50/51)*(1/53)=52/(51*53)=52/2703

or about 0.0192378838327783943 rather than the 0.0192307692307692307 that 1/52 would be.

 Posted by Charlie on 2004-02-05 08:43:55

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