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How often does he lie? (Posted on 2004-07-02)

In the "Not-always-lying politician" problem, what's the probability that a particular sentence is true?

See The Solution Submitted by Federico Kereki

Rating: 2.5000 (4 votes)

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re: Solution

| Comment 2 of 8 |

(In reply to Solution by Bob)

It's true that the probability of a sentence being true is 70.8333... percent if the politician is equally likely to have followed any one of the 144 possible ways he could make ten statements. That's verified by this program:

DECLARE SUB addon (s$)
DIM SHARED tCount, fCount, s$
OPEN "truefals.txt" FOR OUTPUT AS #2

addon s$

PRINT tCount, fCount
PRINT #2, tCount, fCount

SUB addon (s$)
s$ = s$ + "t"
IF LEN(s$) < 10 THEN
    addon s$
ELSE
    PRINT #2, s$
    FOR i = 1 TO LEN(s$)
      IF MID$(s$, i, 1) = "t" THEN tCount = tCount + 1: ELSE fCount = fCount + 1
    NEXT
END IF
s$ = LEFT$(s$, LEN(s$) - 1)

IF RIGHT$(s$, 1) <> "f" THEN
    s$ = s$ + "f"
    IF LEN(s$) < 10 THEN
      addon s$
    ELSE
      PRINT #2, s$
    FOR i = 1 TO LEN(s$)
      IF MID$(s$, i, 1) = "t" THEN tCount = tCount + 1: ELSE fCount = fCount + 1
    NEXT
    END IF
    s$ = LEFT$(s$, LEN(s$) - 1)
END IF
END SUB

which prints out the ways and tabulates the total true and total false:

tttttttttt
tttttttttf
ttttttttft
tttttttftt
tttttttftf
ttttttfttt
ttttttfttf
ttttttftft
tttttftttt
tttttftttf
tttttfttft
tttttftftt
tttttftftf
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ttttfttftt
ttttfttftf
ttttftfttt
ttttftfttf
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tttftttttt
tttftttttf
tttfttttft
tttftttftt
tttftttftf
tttfttfttt
tttfttfttf
tttfttftft
tttftftttt
tttftftttf
tttftfttft
tttftftftt
tttftftftf
ttfttttttt
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ttfttttftt
ttfttttftf
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ttfttftttt
ttfttftttf
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 1020          420

However, if the politician wants to lie as much as he can he will just alternate truths and lies without regard for the other possibilities, and each statement will have a 50% chance of being true.

Posted by Charlie on 2004-07-02 15:15:02

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