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This is a true story, and an illustration of smart thinking.

During WWII, Allied airforces were having a difficult time getting their bombers to withstand German artillery. Their planes desperately needed some armour to increase the chances of them surviving bomb runs. Unfortunately armour is heavy, so it could only be applied in specific areas where it was absolutely needed.

A mathematician named Abraham Wald examined the surviving planes, making a note of where the artillery damage was most severe. The military felt these damaged areas were obviously the most vulnerable parts of the plane and therefore should should have the armour applied to them. Wald, however, recommended that armour be added to the areas that hadn't been damaged by the artillery fire.

Why?

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Because ...

... the examined planes made it home more or less safely. That means that the holes weren't critical.

On the other hand, the planes that were shot down and therefore couldn't be examined were hit in other places — the places that could probably do with some extra armour.

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  • $\begingroup$ Does luck/chance not play a role here :-) ? $\endgroup$
    – Mea Culpa Nay
    Nov 18, 2017 at 14:00
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    $\begingroup$ @MeaCulpaNay you can think of it as a sort of Monte Carlo simulation of where planes can survive getting shot. There is some luck, sure, but the aggregate effect is what matters. $\endgroup$
    – fectin
    Nov 18, 2017 at 18:42

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