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Topic: Psychic Friends Network (Read 575 times) |
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TimK
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Psychic Friends Network
« on: Oct 13th, 2004, 7:37am » |
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A fair coin is flipped and then hidden. Molly has an 80% chance of guessing the state of the coin (heads or tails), Spike has a 70% chance, while poor Waldo only has a 10% chance of a correct guess. Basil wants to devise a scheme using all of these guesses to predict the state of the coin. What level of accuracy does the best scheme give?
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Grimbal
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Re: Psychic Friends Network
« Reply #1 on: Oct 13th, 2004, 7:58am » |
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It would be at least 90%. For more, we need to know how independent the guesses are.
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towr
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Re: Psychic Friends Network
« Reply #2 on: Oct 13th, 2004, 9:59am » |
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If the guesses are independant, I'd say :: 99.4% ::
But I haven't really worked that out properly, so chances are it's wrong.
::poor Waldo, he should just invert his guess, to get 90% accuracy..::
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TimK
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Re: Psychic Friends Network
« Reply #3 on: Oct 13th, 2004, 10:30am » |
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The guesses are completely independent.
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Fresno_Bob
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Re: Psychic Friends Network
« Reply #4 on: Oct 13th, 2004, 10:35am » |
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Assuming independence, here are the possibilities...
agreement Waldo right Waldo wrong
WSM/0 .1 .7 .8 .9 .3 .2
SM/W .1 .3 .2 .9 .7 .8
WM/S .1 .3 .8 .9 .7 .2
WS/M .1 .7 .2 .9 .3 .8
or
agreement Waldo right Waldo wrong
WSM/0 .056 * .054
SM/W .006 .504 *
WM/S .024 .126 *
WS/M .014 .216 *
Best scheme should take max of each row, indicated by *,
giving 90.2%
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towr
wu::riddles Moderator
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Re: Psychic Friends Network
« Reply #5 on: Oct 13th, 2004, 10:35am » |
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after properly working it out (I hope), I get ::90.2%
And the scheme is as follows: go with the opposite of what Waldo guesses, unless all three agree::
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TimK
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Re: Psychic Friends Network
« Reply #6 on: Oct 13th, 2004, 10:41am » |
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towr,
Waldo's accuracy of 10% takes into account the fact that sometimes he guesses the opposite of what he really thinks, because he realizes he's really bad at this 
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towr
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Re: Psychic Friends Network
« Reply #7 on: Oct 13th, 2004, 12:07pm » |
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That doesn't change the scheme though, it's just a sad reflection of Waldo's fate..
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