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Fooled by Randomness

Tangled up in Blue

Certified Senior Citizen⭐
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If a test for some disease is 95% accurate,and the disease affects one person in a thousand,and you go for a test and it comes back positive,what's the probability that you have the disease?

Answers and your reasoning please.
 
If a test for some disease is 95% accurate,and the disease affects one person in a thousand,and you go for a test and it comes back positive,what's the probability that you have the disease?

Answers and your reasoning please.
about 2% - reason, I'm right because I always am x
 
If a test for some disease is 95% accurate,and the disease affects one person in a thousand,and you go for a test and it comes back positive,what's the probability that you have the disease?

Answers and your reasoning please.

A test can't be 95% accurate, a diagnostic test is defined by sensitivity and specificity.

Sensitivity = The probability of getting a TRUE POSITIVE. i.e. the probability of the test saying positive when the person has the disease

Specificity = The probability of getting a TRUE NEGATIVE. i.e. the probability of the test saying negative when the person doesn't have the disease.

A 100% accurate test (i.e. 100% sensitivity and specificity) will mean that there are never any false positive or false negative results.

I assume that in your question you can't have false negatives, but I'll let someone else solve it because this is what I do for a day job.
 
about 2% - reason, I'm right because I always am x

Correct but I don't agree with your reasoning. :raspberry:
"The correct answer is 2 per cent,because if you test 1,00 people,the test will give fifty positives,whereas only one of the population actually has the illness."
John Lanchester.Whoops!(Thanks to Yogi for the heads up on this excellent book).:thumbsup:
(eg drawn from Taleb's Fooled by Randomness).
 
If a test for some disease is 95% accurate,and the disease affects one person in a thousand,and you go for a test and it comes back positive,what's the probability that you have the disease?

Answers and your reasoning please.

If your test is positive, and the test is 95% accurate, then there is a 95% chance that you have the disease. The fact that it affects one in a thousand, one in a hundred, even one in two, is irrelevant. Obviously to derive the accuracy rate of 95%, all people that tested positive were then monitored to see how many actually had the disease, and it came to 95%. You are bringing in a further factor which has nothing to do with the probability.
I thank you.
 
If your test is positive, and the test is 95% accurate, then there is a 95% chance that you have the disease. The fact that it affects one in a thousand, one in a hundred, even one in two, is irrelevant. Obviously to derive the accuracy rate of 95%, all people that tested positive were then monitored to see how many actually had the disease, and it came to 95%. You are bringing in a further factor which has nothing to do with the probability.
I thank you.
well at least one person fell into the trap!
 
191389-pi_350.jpg
 
I'm glad you are reading Taleb, Barna. Hopefully it will demonstrate to you why socialism and planned economies are intellectually bankrupt.
 
I'm glad you are reading Taleb, Barna. Hopefully it will demonstrate to you why socialism and planned economies are intellectually bankrupt.

Neil,
You missed the point.He's quoted in John Lanchester's "Whoops!:Why everyone owes everyone and no one can pay".I suspect JL is (secretly) one of my lot.
 
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