Bayes Theorem Question - Am I doing this right?

[RedPhoenix]

Another Conditional Problem...

Lie Detector is
95% reliable when the person is guilty
98% reliable when innocent

Random Person pulled from a pool of people... This pool is 6% guilty of theft and 94% have never stolen...

Random person was determined guilty from the lie detector, what is the probability he is innocent?

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My attempt...

(.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7512 . so 75.12% chance of him being guilty. Seems low, but I guess the fact that the pool of people has only 6% guilty in it, it lowers the chance a lot.

 

[lurflurf]

I get
(.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7520
This is a famous paradox
If a test is fairly accurate, but the population mostly negative a positive test is not very reliable.

 

[RedPhoenix]

I get
(.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7520
This is a famous paradox
If a test is fairly accurate, but the population mostly negative a positive test is not very reliable.

Pretty crazy, but thanks for the help :)