I'm glad we arrived at he same answer. I suppose lil will have a bit easier time following your logic. I had only read the bullet points from your post, and not the text of the book page, so I think I may have rehashed some unnecessary stuff. Anyway, lil, the main point is that there are a lot of counter intuitive things in statistics.
Yes, and our number agrees with the footnote in the book, but I still don't follow the explanation there. Where did the number 1.706 come from? Simpson's Paradox is my favorite statistical anomaly.
I'm not sure either. I had tried to manipulate the equation to read something of the form P(A)/(1 + P(A)), but I couldn't find an obvious way to do that. Also, it doesn't work the other direction. That is, the probability of the car being green when it's reported green does not equal the probability of the car being reported blue divided by 1 plus that probability, so it's certainly not a general solution to the problem, but perhaps a weird coincidence of the way he did the arithmetic.Where did the number 1.706 come from?