started to study a bit late for the exam, so bear with me please.
We always do 2 tests to check if a player is doped. If he's doped for first test will give us 100% success that he's doped and the second test only gives us 70%, so 30% of doped players don't get detected. But if a un-doped player gets testet the chances are 15% that the first test is positiv anyway, so 10.5% ?? of un-doped players get tested positive. What's the percentage of doped players?
My idea was, to have the state of being doped as the condition for the probability. isClean = C and isDoped. So, if he's truly doped, then there's a 0.7 chance that he gets tested positive. If he's clean, then there's still a 0.105 chance that he's positive, right? That's how far I've gotten.
-> so, if he's doped, then P(D|D)? That make's no sense to me. I also get confused how to apply it to the main population.