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I'm trying to solve the question which is quite basic using confusion matrix but my solution is not matching the correct solution.

Q: Let's say we have a drug test that can accurately identify the users of a drug 99% of the time, and accurately has a negative result for 99% of non-users. But only 0.3% of the overall users use this drug.

What are the odds of someone being an actual user of the drug given that they tested positive?

Also, is TP / (TP + FN) is same as P(A) P(B|A)/P(B) ?

My Approach:

                                TP      TN        Total
Users       Predicted positive   29.7      0.3       30
Non-Users   Predicted negative   99.7   9870.3     9970
                                129.4   9870.6    10000

From the above data, I got : 29.7/129.4 = 0.2295208655 around 22.95%

But the solution states : 22.8% . I'm confused. What is the right way to do this?

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1 Answer 1

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I got it :

The approach which was given was something like this - P(B) is 1.3% ( 0.99*0.003 + 0.01*0.997) So, P(B|A) = P(A) P(B|A) / P(B) = 0.003*0.99 / 0.013 = 0.228 . So, '22.8%'

But they have rounded the number to 1.3% instead of 1.294% and that's why the value is different!!

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