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.