Very Rare

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Frequently Asked Questions...

How do I determine the needed sample size for a 95% confidence in the exact probability of a very rare event?

I have an event that occurs, and is very rare. Say the sample thusfar is 9 positives out of 90,000 trials. How would I determine how many trials I would need to have 95% confidence in the estimated probability (which appears currently to be 1 in 10,000, or 0.01%)? Assume this event is completely random. The only question that remains is what the true probability is.


Best Answer...

Answer:

There is no such number; this is a misunderstanding of confidence intervals.

The confidence interval really applies to the *error*, not to the *mean*. In other words, you might be able to say "With 95% confidence, the true probability lies between 0.009% and 0.011%" (a ±10% error). But you can never say "I'm 95% sure that the probability is *exactly* 0.01%."