If the probability is 1:1,000,000, then in one million experiments there is a finite probability (1:1,000,000) that you may see the event once, and a lesser finite probability you would see it more than once.
Who ever moded this mathematically ignorant fool insightful?? It's ok if you are engineers, programmers and nerds, but people, we are talking about elementary statistics here...
Let the probability of an event be p=10^-6 . And let's do 10^6 independent repetitions of the experiment.
First, the probability that you'll see the event _once_, is
(10^6 choose 1)*(10^-6)^1*(1-10^-6)^(10^6-1) ,
which is about e^-1 , which is about 0.3679 . Which is of course far greater than 10^-6 .
Second, the probability that you'll see the event _more than once_, can be easily calculated via binomial theorem, or just plain common sense, to be
1-(above)-(1-10^-6)^10^6 ,
which is about 1-2/e , which is about 0.2642 .
I hope that clarifies some things.
