Risk of plane bombs

A mathematician and a non-mathematician are sitting in an airport hall waiting for their flight to go. The non has terrible flight panic.

Hey, dont worry, its just every 10000th flight that crashes.

1:10000? So much? Then it surely will be mine!

Well, there is an easy way out. Simply take the next plane. Its much more probable that you go from a crashing to a non-crashing plane than the other way round. So you are already at 1:10000 squared.

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