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simon,
Actually, I think it might (though I'm obviously open to correction) if you take the anthropic principle as a given (which I do not).
One thing you're missing is that there are two events here, call them A and B:
A. LHC would destroy earth B. LHC works
So the events, which are NOT independent, should look more like:
- The LHC would destroy earth, and it fails to operate
- The LHC would destroy earth, and it works
- The LHC would not destroy Earth, and it fails to operate
- The LHC would not destroy Earth, and it works
Outcome 2 is "closer" to outcome 1. More precisely, evidence that 2 occured would increase our probability of both A and B, which would therefore decrease the probability of event 3 relative to event 1.
The fact that 2 is invisible means that we can't tell when it has happened. But there is a chance that it is happening that would increase with each subsequent failure, as Eliezer noted.
This is far from formal but I hope I'm getting the gist across.