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How often does he lie? (Posted on 2004-07-02) Difficulty: 3 of 5
In the "Not-always-lying politician" problem, what's the probability that a particular sentence is true?

  Submitted by Federico Kereki    
Rating: 2.5000 (4 votes)
Solution: (Hide)
Call S(i) the number of valid sequences of i statements; as per the solution of the other problem, S(1)=2, S(2)=3, S(3)=5, and generally, S(i)=S(i-2)+S(i-1).

Call F(i) the total number of false statements taking into account all the possible sequences in S(i); F(1)=1, F(2)=2, and in general, F(i)=F(i-1)+F(i-2)+S(i-2). [To see why, see the solution to the other problem]

The average of false sentences is F(i)/(i*S(i)), which experimentally converges to about 0.27... [more on this to follow] so the answer we are looking for is 0.73... or 73%.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionGiven answer is wrong!Math Man2012-05-16 09:25:43
Solutioni c it this wayAdy TZIDON2004-07-03 02:09:44
SolutionA different takeTristan2004-07-02 15:37:22
MaybeMax2004-07-02 15:37:21
re: SolutionCharlie2004-07-02 15:15:02
Some ThoughtsSolutionEric2004-07-02 14:49:49
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