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Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
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PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.
With the drug testing, they now do A and B samples - so if sample A comes back positive, they then test the B sample. This is an added layer to prevent the innocent being found guilty, but I guess it comes down to what made them test positive in the first place. If it's a simple dice-roll random chance thing, then the B sample is 95% likely to then prove a wrongly accused person not-guilty - but if it's something else (perhaps the drug test looks for markers in their urine which usually signify drug taking but in 5% of the population is natural), then they're still in trouble!
If it's the first case, then with a second test your 590 athletes who test positive in sample A (495 innocent, 95 guilty) becomes 115 (25 innocent 90 guilty) which gives 78% chance of getting the guilty. A bit more palatable.