How do you hold the small odds against the big dread?

I spent the evening looking at a world map of every commercial airline crash ever recorded — thousands of tiny dots, each one somebody's last ordinary Tuesday. In my line of work I deal in rare catastrophic events that are never supposed to happen, and I still haven't figured out how people truly weigh a 1-in-11-million chance against the weight of their own death. Do you actually believe the statistics when you buckle in, or do you just override that part of your brain?