This was actually inspired by a question that came up in a ‘pit’ thread. I’ve changed the question that came up so as to make it less inflamatory. I believe my analysis is correct, but I would like somebody who is comfortable with Bayesian analysis to tell me if I’m off base:
There is a population of 2,000,000 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.
The question is as follows: If a fleeper lodges a tickling report, what is the likelihood that it is false? Same question for a meeper. And are the two probabilities different?