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It is known that 0.2 percent of the population is HIV positive. A screening test for HIV has a 10 percent chance of incorrectly showing positive when the subject is negative. and a 2 percent chance of incorrectly showing negative when the subject is positive. What proportion of the population that tests positive has HIV?

Dat Ba Tran
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  • This is an exercise in conditional probability and not particularly difficult - what have you tried? What numbers would you expect if there were $1$ million people in total? – Henry Sep 18 '21 at 15:40
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    You need to show what you have tried, and where you are stuck, or what is troubling you about this problem. – true blue anil Sep 18 '21 at 16:00
  • If you aren't familiar with these types of problems, see Bayes Theorem. – user2661923 Sep 18 '21 at 16:08
  • See whether this tree diagram helps you understand/solve your exercise. – ryang Sep 18 '21 at 16:24
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    @RyanG I claim foul. I copyrighted the word Addendum. – user2661923 Sep 18 '21 at 16:30
  • @RyanG In your cited answer, you used the word Addendum. This is the only time, on mathSE, that I have ever seen anyone besides myself use that word. – user2661923 Sep 18 '21 at 16:34
  • @user2661923 Well, given that I'm the longer-time member, I have a greater probability of being the actual, erm, trailblazer! In all seriousness, this was likely the first such instance. Perhaps you could claim to be the first to boldface it? – ryang Sep 18 '21 at 16:57

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