On Saturday 13 March 2010, erythrocyte wrote: > On Sat, Mar 13, 2010 at 1:14 PM, Robert J. Hansen <r...@sixdemonbag.org>wrote: > > Even then — so what? Let's say the Type II rate is 25%. That's a > > very high Type II rate; most people would think that failing to > > recognize one set of fake IDs per four is a really bad error rate. > > Yet, if you're at a keysigning party where there are five people > > independently applying a 25%-faulty test, the likelihood of > > accepting a fake ID is under 1%. > > It really depends on how you're calculating combined probability. If > you take an example of 4 individuals at a keysigning party, > > The combined probability that all individuals would accept a fake ID > would be 1/4 * 1/4 * 1/4 * 1/4 = 0.00390625 . > > However, the combined probability that at least one of the encounters > would result in accepting a fake ID would be 1/4 + 1/4 + 1/4 + 1/4 > = 1 . > > Please do correct me if I've made a mistake. I'm not a math guru by > any means.
Sorry, but your calculation is wrong. If the calculation was correct then with 5 encounters the probability would be 1.25 which is an impossibility. Probability is never negative and never > 1. (People say all the time that they are 110 % sure that something will happen, but mathematically that's complete nonsense.) The probability that the fake ID is rejected by all individuals is (1 - 1/4)^4. Consequently, the probability that the fake ID is not rejected by all individuals (i.e. it is accepted at least by one individual) is 1 - (1 - 1/4)^4. Regards, Ingo
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