A defendant is being tried for murder and the only evidence against him is that a tissue sample from the scene matches his. The prosecution believe that there is a 1/10,000 chance of making that match by chance.It is known the guilty party lives in a village of 35,000 people. The defendant is also from that village. Use Bayes' Theorum to work out the probability that the defendant is innocent. Highlight any assumptions you make.
Pr(Innocent|Village) = Pr(Village|Innocent) Pr(Innocent) / Pr(Village)
If you take Pr(Village) = 1
With Pr(Village|Innocent) = 34999/35000
Pr(Innocent) = 1/10000
You get Pr(Innocent|Village) = 0.01%
That's what I've tried, using Bayes, but I'm just a little hazy on whether or not I've got the right Pr(Village|Innocent) and Pr(Village), where I've made the assumption the Population is closed to that of the Village...
Read this: Prosecutor's fallacy - Wikipedia, the free encyclopedia and related pages found using Google.