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Changing aces (Posted on 2005-01-31) Difficulty: 2 of 5

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?

See The Solution Submitted by Steve Herman    
Rating: 3.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution I think... | Comment 4 of 9 |

Um... I really think that there is no correct answer! The first answer i came up with was this: Q1:25% Q2:50% Q3:75%-- the after that i was thinking then i thought maybe all the answer to all of the questions is 75%--- but then again i was thinking and i decided that- since on Q1 it  revealed that only 1 player's face revealed that his card was different so i thought.. then i was like OMG it has to be 25% because there are 4 players and only 1 player revealed that his card was different!-- Then i thought about Q2 it revealed that another player's face revealed his card was also different! So that makes 2 which is 50%!!-- then on Q3 it revealed that again another players face revealed that his card was also different!! So wala! The answer is: Q1-25% Q2-50% Q3-75% so the answer is he has a 75 pecent chance his is different! But there is still a 25% chance it is the smae! Be cause the other players could have got there cards switch but his could be the same!


  Posted by Kelsey on 2005-02-02 17:11:51
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