ChatterBank0 min ago
Riddle me this ....................
5 Answers
Consider the following (fictional) facts:
1. 1% of women at age forty who participate in routine screening have breast cancer.
2. 80% of women with breast cancer will get positive mammographies.
3. 9.6% of women without breast cancer will also get positive mammographies.
Question: A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
Apparently, most doctors get the same wrong answer on this problem - usually, only around 15% of doctors get it right. Let's see how you ABer's do - I'm sure you're all far more intelligent than Doctor Jones from down the road .............
1. 1% of women at age forty who participate in routine screening have breast cancer.
2. 80% of women with breast cancer will get positive mammographies.
3. 9.6% of women without breast cancer will also get positive mammographies.
Question: A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
Apparently, most doctors get the same wrong answer on this problem - usually, only around 15% of doctors get it right. Let's see how you ABer's do - I'm sure you're all far more intelligent than Doctor Jones from down the road .............
Answers
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Out of 100 women 1 will have it, 99 won't.
For every 1 person that has it there 0.8 women will get a positive result and 0.2 will get a negative result.
For the 99 that don't have it 9.5 will get a positive result and 89.5 will get a negative result. (All figures to one decimal place.)
Altogether, taking all 100 women, 10.3 will get a positive result and 89.7 will get a negative result.
So, for someone with a postive result the chances of actually having breast cancer are 0.8 out of 10.3, which as a rounded percentage is 7.8%
For every 1 person that has it there 0.8 women will get a positive result and 0.2 will get a negative result.
For the 99 that don't have it 9.5 will get a positive result and 89.5 will get a negative result. (All figures to one decimal place.)
Altogether, taking all 100 women, 10.3 will get a positive result and 89.7 will get a negative result.
So, for someone with a postive result the chances of actually having breast cancer are 0.8 out of 10.3, which as a rounded percentage is 7.8%
Correct.
Like I said, "I'm sure you're all far more intelligent than Doctor Jones from down the road ............."
The problem is taken from the following website and explained in full:
http://yudkowsky.net/rational/bayes
Like I said, "I'm sure you're all far more intelligent than Doctor Jones from down the road ............."
The problem is taken from the following website and explained in full:
http://yudkowsky.net/rational/bayes
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