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I have a hard time grasping gamblers fallacy. When you flip a coin 100 times and it shows heads, flipping it again results always in a 50-50 chance for heads an tails. That is kind of logical, because past events cannot influence current outcomes. Furthermore, you don't know how the coin was flipped before the start of your experiment. It could have shown 300 heads in a row, which again would not have any influence on the current outcome. If it were this way, possibility as we know it can not exist (every coin would be 'rigged' in the sense that all past flips had to be accounted for).

Now comes the part where I'm struggling: In some professions, there are 2 negative Covid tests required. But when i take one test and it's negative, why does the second test matter? Shouldn't it be also the same possibility as when I took the first test?

brandbenni
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  • I would speculate that Test-1 can result in a false negative if (an unusual) condition-1 happens to be met, and Test-2 can result in a false negative if (an unusual) condition-2 happens to be met. Then, two scenarios come to mind: [1] Condition-1 and Condition-2 are incompatible with each other, in which case at least one of the Test-Negative results had to be accurate: or [2] The chance of Condition-1 and Condition-2 both existing in the same person are deemed extremely remote, so that the Health Department has deemed the possibility as one to be ignored. – user2661923 Sep 18 '21 at 23:12
  • Re previous comment, speculating in a vacuum, plausible scenario alternatives are [3] if Condition-1 and Condition-2 both exist in the same person, then the person can't spread the disease : or [4] if Condition-1 and Condition-2 both exist in the same person, then the person has some built in immunity which will render the disease harmless in that person. Scenario [4] however might still allow the disease to be spread, so this one is iffy. – user2661923 Sep 18 '21 at 23:16
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    The critical assumption about coin flips is that they are independent of each other, but covid tests are very much not. Otherwise you might as well flip a coin instead. Also, real world medical tests are not $100$% accurate. – Somos Sep 18 '21 at 23:33
  • @Somos : "Also, real world medical tests are not 100% accurate" : ironically, ambiguous, but true, no matter what you intend. One interpretation is if the exact same test is done by two labs, you could get two results, because one of the technicians was negligent. The other interpretation is that you are assuming that no negligence occurs, but that medical tests are (for example) prone to false positives or false negatives. Then, it could be argued that Test-1-Negative might be a true-Negative or False-Negative, and ditto for distinct Test-2. ...see next comment – user2661923 Sep 19 '21 at 05:11
  • Then, it could be argued that Test-1-Negative + Test-2-Negative is either two true-Negatives (on semi-unrelated tests) or two false-Negatives. Then, it could be argued, that in this case two true-Negatives is exponentially greater than one true-Negative. This means that two false-Negatives is exponentially less than one false-Negative, re the two tests are distinct. Does one of these two interpretations (negligent technician on repeated test OR two distinct types of tests) accurately represent what you were intending to convey? – user2661923 Sep 19 '21 at 05:15
  • I was thinking about the interpretation of false positives or negatives, not a negligent technicians. But, as @Somos mentioned, I think the key of the problem is that two medical tests are not independent from each other. – brandbenni Sep 19 '21 at 09:29

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