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        riddles >> putnam exam (pure math) >> Bayesian Question
        
(Message started by: THUDandBLUNDER on Aug 14^th, 2006, 9:33pm)

Title: Bayesian Question
Post by THUDandBLUNDER on Aug 14^th, 2006, 9:33pm

Saw this on another site and, as I have no time to have a go at it myself, I thought I would chuck it in towr's (et al) direction:

;)

There is a population of 1,000,000 people made up of 1,000,000 fleepers and 1,000,000 meepers.

There is an offense among these people known as tickling. However, fleepers only tickle meepers; and meepers only tickle fleepers.

Every time a person is tickled, he reports it to the Tickling Authority who investigates the claim.

Unfortunately, there are also a large number of FTR's: False tickling reports. It is known that 25% of all tickling reports are false.

Every year, the Tickling Authority receives approximately 13,333 tickling reports.

Two other facts of note: For reasons that are not entirely clear, there is a tremendous imbalance in the incidence of tickling in the two populations:

99% of tickling incidents involve fleepers tickling meepers. Only 1% go the other way. (These are tickling incidents that are investigated and confirmed by the tickling authority.)

Lastly, members of both groups are equally likely to lie. Thus, a fleeper that has not been tickled is just as likely to file an FTR (false tickling report) as a meeper who has not been tickled.

1) If a fleeper lodges a tickling report, what is the likelihood that it is false?

2) If a fleeper lodges a tickling report, what is the likelihood that it is false?

3) As members of both groups are equally likely to lie, can we infer that the reporting of tickling is equally distributed between the two groups?

Title: Re: Bayesian Question
Post by towr on Aug 15^th, 2006, 1:27am

[hideb]A meeper's report has +/- 14.4% chance to be false
A fleeper's report is false with about 94.3% probability.

If both groups are equally likely to file false reports, then we'd expect +/- 1667 false reports from each group. But from the 10000 valid reports, meepers make 99%, whereas the fleepers make 1%. So the reports are not equally distributed.[/hideb]