Here you go: Please state your answer as a percentage (If you know what the solution is and why, don't give the reason away right away, just give the answer along with a smiley and text saying you know but won't tell - I want people to think on this one. Also - I've made it as easy as I can to arrive at the right answer.) A man goes to see his doctor for his standard annual checkup. As part of the standard checkup, the doctor performs a test that has 99 percent reliability - that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?
Someone post the answer but use spoiler tags - that'll mean no accidental views. p.s. I'm a whisker short of the answer, I know vaguely, but not fully.
Got it (thanks to ch424 for giving me the answer Spoiler of 50% , - had to practically work it out to 'GET IT' though ) Spoiler sick 1% of population false negative (1% of those sick) = 0.01% of population ( 0.01(sick) x 0.01(falseresult) ) positive (99% of those sick) = 0.99% of population ( 0.01(sick) x 0.99(accurateresult) ) Well 99% of population False positive (1% of those well) = 0.99% of population ( 0.99(well) x 0.01(falseresult) ) negative (99% of those well) = 98.01% of populaton ( 0.99(well) x 0.99(accurateresult) So 0.99% of the general population would have a positive, and 0.99% would have a false positive. Hence, 50% of those that test postive are actually negative.
This is my working: Spoiler P(positive|sick) = 0.99 P(negative|sick) = 0.01 P(positive|well) = 0.01 P(negative|well) = 0.99 P(sick) = 0.01 P(well) = 0.99 Therefore: (A) P(positive) = 0.99x0.01 + 0.01x0.99 and (B) P(sick AND positive) = P(positive|sick)xP(sick)=0.99x0.01 and (C) P(sick AND positive) = P(sick|positive)xP(positive) sub values from (A) and (B) into (C) 0.99x0.01 = P(sick|positive)x0.99x0.1x2 Therefore P(sick|positive) = (0.99x0.01)/(0.99x0.01x2) = 1/2 = 50%
Well - either ch424 very recently took a class on the subject, or he took the answer straight off the web as he quoted the equations for Bayes' theorem exactly verbatim - but yeah, the answer is exactly 50% genesisofthesith did a very thorough and clear job of explaining it in his post. After a day or so - why don't you remove those spoiler tags, but leave them up for a bit....
Yep, exactly Dream. I took a class on statistical mechanics last semester, but that seems such a long time ago!
We covered Bayes' theorem two years ago in maths at school. There's a question like that in every single S1 paper, so I'm used to doing them. I wouldn't cheat, I'm not a moron. However, kudos to genesisofthesith for the elegance of his answer!
