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army1987 comments on The Fallacy of Large Numbers - Less Wrong Discussion
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It is. The problem is that 3 isn't large. Having 10000 cars and 0.03% failure rate would give almost exactly the same probability distribution for the number of cars broken on a given day (namely, the Poisson distribution with lambda=3). Even for N = 20 and p = 15% the Poisson distribution would be a decent approximation.
If you have 100 cars and there's a 50% failure rate, there'd be a standard deviation of five, so you'd need an extra 15 or so cars to be safe. You have to give up almost a third of them. Three not being large is the bigger problem, but 100 still isn't all that large.