But I think the probability calculation you cite toward the end is not correct. If the probability of making amistake in a given scroll and word is p then the probability of exactly 1 of 3 being wrong on a particlar word is 3*p*(1-p)^2 and the probability of 2 of 3 wrong is 3*p^2(1-p). Given that you have three scrolls that split 2:1 the probability that the majority is wrong is: 3p^2*(1-p)/((3 p (1-p) (p+(1-p))) which equals p. If there are three disagreements the probablilty that the majority is right in all three (assuming mistakes are uncorrelated) is (1-p)^3. If we assume, based on the fact that all the other words agree, that p is something like 1/(number of words in a scroll, i.e, about 80,000) then the chance that Ezra had the correct text (assuming the only possible errors were the places where the 3 scrolls differed) would be greater than 99.99%. (The probablilty that all three would have the same mistake in one word is negligible) Even if you assume that mistkes would only be possible in a small fraction of the words, the probability that majority is right in all 3 cases is fairly large. If there are only 800 words that could have mistakes (p=1/800) the probability that all three are right still exceeds 99.5%, assuming errors are uncorrelated. Of course, given the discrepencies between the gemara's text and the Massoretic Text, we know a greater number of differences have come in since. Especially since the middle letter etc. in our scrolls does not match what it is supposed to. But if we go by the gemara about the three scrolls in that Azara found in Ezra's time, it is highly likely that the majority in each case had the correct text.