Author |
Topic: Psychic Friends Network (Read 546 times) |
|
TimK
Newbie
Gender: 
Posts: 30
|
 |
Psychic Friends Network
« on: Oct 13th, 2004, 7:37am » |
 Quote  Modify
|
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?
|
|
 IP Logged |
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Psychic Friends Network
« Reply #1 on: Oct 13th, 2004, 7:58am » |
Quote Modify
|
It would be at least 90%. For more, we need to know how independent the guesses are.
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Psychic Friends Network
« Reply #2 on: Oct 13th, 2004, 9:59am » |
Quote Modify
|
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..::
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
TimK
Newbie
Gender:
Posts: 30
|
|
Re: Psychic Friends Network
« Reply #3 on: Oct 13th, 2004, 10:30am » |
Quote Modify
|
The guesses are completely independent.
|
|
IP Logged |
|
|
|
Fresno_Bob
Newbie
Gender:
Posts: 13
|
|
Re: Psychic Friends Network
« Reply #4 on: Oct 13th, 2004, 10:35am » |
Quote Modify
|
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%
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Psychic Friends Network
« Reply #5 on: Oct 13th, 2004, 10:35am » |
Quote Modify
|
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::
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
TimK
Newbie
Gender:
Posts: 30
|
|
Re: Psychic Friends Network
« Reply #6 on: Oct 13th, 2004, 10:41am » |
Quote Modify
|
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 
|
|
IP Logged |
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Psychic Friends Network
« Reply #7 on: Oct 13th, 2004, 12:07pm » |
Quote Modify
|
That doesn't change the scheme though, it's just a sad reflection of Waldo's fate..
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print