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        riddles >> easy >> Psychic Friends Network
        
(Message started by: TimK on Oct 13^th, 2004, 7:37am)

Title: Psychic Friends Network
Post by TimK on Oct 13^th, 2004, 7:37am

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?

Title: Re: Psychic Friends Network
Post by Grimbal on Oct 13^th, 2004, 7:58am

It would be at least 90%. For more, we need to know how independent the guesses are.

Title: Re: Psychic Friends Network
Post by towr on Oct 13^th, 2004, 9:59am

If the guesses are independant, I'd say ::[hide] 99.4% [/hide]::
But I haven't really worked that out properly, so chances are it's wrong.

::[hide]poor Waldo, he should just invert his guess, to get 90% accuracy..[/hide]::

Title: Re: Psychic Friends Network
Post by TimK on Oct 13^th, 2004, 10:30am

The guesses are completely independent.

Title: Re: Psychic Friends Network
Post by Fresno_Bob on Oct 13^th, 2004, 10:35am

[hide]
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%

[/hide]

Title: Re: Psychic Friends Network
Post by towr on Oct 13^th, 2004, 10:35am

after properly working it out (I hope), I get ::[hide]90.2%
And the scheme is as follows: go with the opposite of what Waldo guesses, unless all three agree[/hide]::

Title: Re: Psychic Friends Network
Post by TimK on Oct 13^th, 2004, 10:41am

towr,

[hide]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 :)[/hide]

Title: Re: Psychic Friends Network
Post by towr on Oct 13^th, 2004, 12:07pm

That doesn't change the scheme though, it's just a sad reflection of Waldo's fate..