[math-fun] The chance that N statistical tests fail simultaneously

Perhaps this nicely typeset page will help you understand the problem: http://rangevoting.org/CombinedTestFail.html The answer is NOT a*b*c*...* despite the tests being independent. This is a trap too many fall into. Indeed, if there were N uniform(0,1) independent randoms, and somebody told you "there exists an ordering such that x_j<j/N for each j=1,2,3,...,N" you do NOT want to be an idiot and conclude "my god, that is an amazingly exponentially improbable miracle." Actually, it is quite likely even for N=100. Eh? So hopefully I've piqued your interest now. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)