Ivor the Engineer
Penultimate Amazing
- Joined
- Feb 18, 2006
- Messages
- 10,643
P(R) = 431840 / 320,000,000 = 0.00135 = 0.135%What is R and M?
Making a wild assumption that R = Rapist and M = Male
If my assumption is true, then you start out by saying that the probability of a person being a rapist given that the person is male is much smaller than the probability of a person being male given that the person is a rapist.
Then bayesian math... and I'm not going to try to turn that into words.
My assumption would seem to be born out by your conclusion that P(M|R) ~ 0.98; we already know that 98% of rapists are males.
Exact answers for the remainder are hard to come by, but they're also not complete unknowns. We have some knowledge and we can make some assumptions. We know for example that P(M|~R) < 0.5. We could arguably say that P(M) = 0.49 if we limit our scope to the US.
And we can proxy P(R). The 2016 National Crime Victimization Survey (NCVS), which measures sexual assaults and rapes that may not have been reported to the police, estimated that there were 431,840 incidents of rape or sexual assault in 2015. With a population of about 320,000,000 in 2015, that puts P(R) at 0.135. Thus P(~R) = 0.865.
So we've got P(M|R) = 0.98, P(M) = 0.49, P(R) = 0.135.
P(R|M) = P(M|R).P(R) / P(M) = 0.98 *0.135/0.49 = 0.27
That would imply that any given male has a 27% chance of being a rapist. That seems high, so let's make the extreme simplifying assumption that the 431,840 instances or rape were committed by only 43,184 males - that would mean that each rapist raped 10 people in 2015, which seems rather high, but we can treat that as a boundary scenario. That would mean that P(R) is more like 0.0135, and we end up with 0.027.
So for any given male, there's between a 2.7% and a 27% chance that they're a rapist.
Therefore P(R|M) = 0.27%, not 27%!
If we include the fact that most rapists are multiple offenders and use 10 as the (reasonable) estimate of the number of rapes they each commit, then:
P(R|M) = 0.027%.
Anyone like to disagree?
