One part of a question like this is kind of easy to answer. How "unlikely" is the specific observation being reported? Obviously the chance of the first 8 digits being even is a little less than 2^-8, a bit under a half a percent. So that seems reasonably surprising.
Disagree! Dealing with infinite sets, the truly "interesting" probabilities are those that occur *despite* zero probability.
But what other observations could have done that? I don't know how to start answering that questien [sic].
How about when you have a barely-converging integral, and you expect a transcendental value but get an integer or rational instead?! As |Z|/|R|=0, you should expect to never draw an integer from a real interval, yet it does sometimes happen. (See other thread: "An Unusual Integral?") --Brad