Question

The city of Midgar is separated quite prominently into to zones: 65 percent of the population lives in the slums while 35 percent live in the plate above. There is a 10 percent chance that a Midgar resident is a Shinra employee given that they live in the plate, while there is a 4 percent chance that a Midgar resident is a Shinra employsee given that they live in the slums. Given that you temporarily incapacitate a Shinra employee to steal their ID card, what is the probability that that person lives in the slums?

Answer 1

P(Shinra Employee)=P(slums)*P(Shinra Employee|slums)+P(plate)*P(Shinra Employee|plate)
=0.65*0.04+0.35*0.1=0.061

therefore P(slums|Shinra Employee)=P(slums)*P(Shinra Employee|slums)/P(Shinra Employee)=0.65*0.04/0.0610 =0.4262