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 Changing aces (Posted on 2005-01-31)

Four different aces are dealt, face up, one apiece, to you and three other players. They are shuffled and redealt, this time face down.

Before looking, the chance is 75% that you have an ace different from your original card.

Question 1) But what if the first player looks at his card and, without showing the card, truthfully reveals that it is not his original ace? What is the chance that you also have a different ace, given that one player's card is known to be different?

Question 2) And what if the second player also looks at his card and, without showing the card, also truthfully reveals that it is not his original ace? What is the chance that you also have a different ace, given that two players' cards are known to be different?

Question 3) Finally, what if the third player also looks at his card and, without showing the card, also truthfully reveals that it is not his original ace? What is the chance that you also have a different ace, given that all three other players' cards are known to be different?

 Submitted by Steve Herman Rating: 3.5000 (4 votes) Solution: (Hide) The 4 aces can be dealt in 24 different ways. Before anybody looks at their cards, your chances of having a new card are 18 out of 24, or 75%. Question 1) There are 18 different ways to deal the cards without giving the first player his original cards, and 14 of the 18 give you a new card also. Probability = 14/18, or 77.77%. Question 2) There are 14 different ways to deal the cards without giving the first two players their original cards, and 11 of the 14 give you a new card also. Probability = 11/14, or 78.57% Question 3) There are 11 different ways to deal the cards without giving the first three players their original cards, and 9 of the 11 give you a new card also. Probability = 9/11, or 81.82%

 Subject Author Date re: Solution Ady TZIDON 2010-02-25 05:58:54 No Subject Narasing Aravind Jay 2005-07-16 18:46:38 Solution jim jones 2005-03-17 07:30:31 My solution Joe 2005-02-09 15:47:08 posting my sol'n - then checking mine against yours John 2005-02-02 22:20:08 I think... Kelsey 2005-02-02 17:11:51 No Subject amee 2005-02-01 00:29:39 re: Solution Charlie 2005-01-31 15:16:14 Solution Jer 2005-01-31 14:22:57

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