How near-complete certainty can make you completely wrong

Ever been asked to go down something beyond a fairish question ? Ever drive part in a grounds in which the grounds is overpowering ? Ever been completely sure you ’re right ? Sure you have . Plenty of meter . So many time that occasionally , you have to have been incorrect .

What would you consider certainty ? In an ideal world , 100 pct certainty would be the only acceptable definition , but as we do n’t live in an idealistic world , settle for nothing less than staring certainty mean not a lot would get done . And so we loosen our standard . We do n’t have to relax them much , but unluckily , even a piddling chip makes a conflict finally .

Let ’s say we set up a exam that gives establishes what we want to find out with a certainty of 99 percent . This examination could establish the guilt or innocence of a defendant , or the presence of a medical condition . It could also establish more complicated thing , like the likelihood that a certain number of crimes in an orbit are committed by one person , or the likelihood that a special drug is effective . All these things can be demonstrate with a 99 percentage certainty . Or , rather , any one of these things can be established with a 99 percent certainty . What if we want to establish all four of these thing ?

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The math is n’t complicated . The likeliness of a coin flip coming up heads is 0.5 . The likelihood of a coin pass coming up heads two times in a row is 0.5 reproduce by 0.5 , or 0.25 . Since a 99 percent chance is 0.99 , we can multiply it by itself the appropriate number of times to get roughly 0.96 , or 96 pct . We are 96 percent certain that all four of the tests are correct . That sounds reasonably honest , except all of those tests are done hundreds of sentence every yr . duplicate 100 multiplication , the probability of the mental test being right falls to 37 pct . Repeated 300 times , and the probability fall to 5 percent . By repeat 450 , and we ’re down to 1 per centum sure thing . In other dustup , we are just as sure that we have get something wrong as we were sure , in each individual showcase , that we got it veracious .

This thought gets a lot of flack , because of the unfortunately large number of people who decide that , “ sometimes tests are wrong , ” means , “ I get to decide that any result I do n’t like is unseasonable . ” The full stop is to let us know the veridical betting odds that sometimes the seemingly incontrovertible test results we get are wrong , and to understand why there is a nonstarter in these trial run . No one has to screw up . No test has to be shoddy . No single case has to be weak . Do something enough , and someone will beat the odds .

[ ViaThe Improbability Principle . ]

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