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Topic: Truth or lie? (Read 1374 times) |
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Altamira_64
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Posts: 116
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Truth or lie?
« on: May 20th, 2013, 7:35am » |
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Alan, Bill, Carl and David are four friends of which each of them tells the truth with probability 1/3, while he lies with probability 2/3.
Alan, Bill and Carl make a statement at this order and then David says that Carl says that Bill says that Alan was telling the truth. What is the probability that Alan was indeed telling the truth?
Clarifications:
Each of them knows when the others tell the truth or are lying.
We only know David's statement, but we know that Bill's and Carl's statements have similar structures.
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towr
wu::riddles Moderator
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Re: Truth or lie?
« Reply #1 on: May 20th, 2013, 9:02am » |
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If i understand it correctly, and worked it out correctly, 13/41
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| « Last Edit: May 20th, 2013, 9:46am by towr » |
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rmsgrey
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Re: Truth or lie?
« Reply #2 on: May 20th, 2013, 11:06am » |
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I agree with towr's answer.
Working:
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There are 16 possibilities for who was telling the truth and who was lying, and 8 of them have David say what he did. In 4 of those, Alan was indeed telling the truth.
The 8 are:
Everybody tells the truth (1/81)
Everybody lies (16/81)
Two people tell the truth (6*4/81)
Giving a 41/81 chance that D says C says B says A told the truth.
The 4 of those 8 where A did tell the truth are:
Everybody tells the truth (1/41)
A and any one other tell the truth (3*4/41)
Total: 13/41 |
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