[chimeracoder]

Time for some fun with binomial probabilities!

Assuming I interpret the actual problem at hand correctly, this is how we formulate it statistically.

We have an event that occurs with probability p = 1/1000000, given an accident (of which there were 13).

The probability of having zero catastrophic events, given that we have observed 13 accidents, is (1-p)^13 = .99987

(For some real hair-raising fun, try this calculation with the success/failure rate of a typical condom.)

Note that this is a purely frequentist interpretation and ignores any Bayesian inference (ie, we assigning a weight of 0 to our Bayesian prior, which is atypical). It's not a very robust way of modeling the situation, for a number of reasons.

[tedunangst]

I think the right test to apply is the Wilson test.