I had to sit down and think things through, but the issue is that the probability that the cab is blue is swapped.

In other words, in the book (and other post), most cabs are green and the Pr(blue) = 0.15. However, here, you assume most cabs are blue and Pr(blue) = 0.85.

If others are trying to look up how the probability was calculated in this book, I thought that I should mention something. So, if others looked this up for the same reason, I wanted to point out why the answers were different: both calculations are right, but the overall frequencies of blue and green cabs are swapped.

Hi,

Thank you for putting together this blog post.

I looked this up because I was reading "Thinking, Fast and Slow" by Daniel Kahneman.

The book reports the correct answer should be 0.41, and that is matched by this blog post:

https://magesblog.com/post/2014-07-29-hit-and-run-think-bayes/

I had to sit down and think things through, but the issue is that the probability that the cab is blue is swapped.

In other words, in the book (and other post), most cabs are green and the Pr(blue) = 0.15. However, here, you assume most cabs are blue and Pr(blue) = 0.85.

If others are trying to look up how the probability was calculated in this book, I thought that I should mention something. So, if others looked this up for the same reason, I wanted to point out why the answers were different: both calculations are right, but the overall frequencies of blue and green cabs are swapped.

Best Wishes,

Charles