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Comment by h2odragon | Hacker News Reader

> requirements are so stringent that many manufacturers, especially bakers, find it simpler and less expensive to add sesame to a product — and to label it — than to try to keep it away from other foods or equipment with sesame.

That's why I always carry explosives when traveling by air: what are the chances that there's two bombs on a plane?

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I remember this one from a youth mathematics book. 10⁻⁴ chance of one bomb, and 10⁻⁸ of two (assuming the other one is an independent event — which it would be, as you're certainly not in collusion with any actual bomber).

Potentially catastrophic false assumption made at the end there.

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.

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.

Those to examples are not at all comparable. The problem with having to keep completely separate facilities for products made with, and products made without sesame is a real problem. And if the law requires that food that is not labeled to have sesame mustn’t be baked in the same oven as products without, then it seems like the easy choice to deliberately add a bit and label it, rather than having to buy new ovens.

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