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        riddles >> medium >> Truth or lie?
        
(Message started by: Altamira_64 on May 20^th, 2013, 7:35am)

Title: Truth or lie?
Post by Altamira_64 on May 20^th, 2013, 7:35am

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.

Title: Re: Truth or lie?
Post by towr on May 20^th, 2013, 9:02am

If i understand it correctly, and worked it out correctly, [hide]13/41[/hide]

Title: Re: Truth or lie?
Post by rmsgrey on May 20^th, 2013, 11:06am

I agree with towr's answer.

Working:
[hideb]
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[/hideb]