What are the odds?

The Bad Science blog explains a statistical fallacy, in the context of a probably wrongfully convicted Dutch nurse:

The judgement was largely based on a figure of “one in 342 million against”. Now, even if we found errors in this figure – and we will – the figure itself would still be largely irrelevant. Unlikely things do happen: somebody wins the lottery every week; children are struck by lightning; I have an extremely fit girlfriend. It is only significant that something very specific and unlikely happens if you have specifically predicted it beforehand.

Richard Feynman had a method for dealing with people who came up with this sort of fallacy. He'd say: "On the way here, I saw the numberplate YH65RE3. What are the chances of that?" In Britain, perhaps one in twenty million...

Spooky.