The number of allergic people in a population of size N can be modeled as a Binomial(N, p) distribution, where p is the probability that any individual person is allergic.

The maximum likelihood estimate for p when we observe 1 allergic person out of 12 is just 1/12, or 8.33%. This is our best guess if we had to name an exact number.

We can get a 95% confidence interval on the value of p using the Clopper-Pearson method with the following R code:

> binom.test(x=1, n=12, p=1/12)
…
95 percent confidence interval:
 0.002107593 0.384796165
…

So we know with 95% confidence that the probability that any individual person is allergic to moon dust is with the range 0.21% and 39%.

Yeah, okay, that’s pretty useless. I agree with them…