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I realize that the answer may well be "Hey, guy, you've just got to learn the math if you really want to understand it" and if so, then so be it, but I thought I'd take a shot.

SO

1) 85% of all cars are blue and 15% are green

2) A witness to an accident says he saw the car involved and it was green.

3) The witness is known to be 80% accurate

Now, what I would take away from that is that the preponderance of blue cars would certainly lower the probability that the car in the accident really was green from 80% to more like maybe 65% or 70%. BUT ... the book says (based on Bayesian statistics) it's 41%. I just can't see how it could be cut it half like that and would appreciate any insight anyone can give me.

Thanks