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Conditional probability doesn’t work like that.

If you always have a bomb with you, then the probability of you sitting on a plane with a bomb is 1, and thus the probability of you sitting on a plane with another bomb is again 10^-4.

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Yes, the post you’re replying to was recounting a joke :)

Indeed. Hmm, but what if I roll a D20 before each flight and take a bomb only if I get a "1"? Do I decrease the average two-bombs probability to 5·10⁻⁶?

Yes. But the conditional probability of the plane having a bomb that’s not yours will still be 10^-4.

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