Is by the very interesting Eliezer S. Yudkowsky. Spend some time on his site. It's good to think.
Why is Bayes important?
Here's a story problem about a situation that doctors often encounter:
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
Next, suppose I told you that most doctors get the same wrong answer on this problem - usually, only around 15% of doctors get it right. Most doctors estimate the probability to be between 70% and 80%, which is wildly incorrect.
What do you think the answer is?
(see below for the answer. See Yudkowsky for why.)
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