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  1. Question-Answer
  2. Quant
  3. factors

Last Updated at October 26, 2022

Question

Data on planes returning from bombing missions was used to study of the vulnerability of airplanes to enemy fire. Analyzing the pattern and frequency of hits from enemy gunfire, it was seen that some parts of planes were hit disproportionately more often than other parts. How could these planes be optimally reinforced with armor plating? There were tradeoffs to consider. Every addition of plating added to the weight of the plane, decreasing its performance. Therefore, reinforcements needed to be added only to the most vulnerable areas of the planes.

Which of the following can be concluded from the above?

CAT 2021

A
The parts hit disproportionately more than the others have to be reinforced as those received the maximum amount of damage.
CORRECT ANSWER WRONG ANSWER
B
No conclusion can be drawn as the data set is incomplete. There is no data on the planes shot down.
CORRECT ANSWER WRONG ANSWER
C
The parts with the least damage have to be reinforced, as the returning planes have survived attacks to the most damaged areas.
CORRECT ANSWER WRONG ANSWER
D
Reinforcements have to be added to all areas of the plane.
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(C)

Explanatory Answer :

This is a real life example of critical reasoning used to solve a military problem during the World War II. A mathematician named Abraham Wald was given this challenging problem by military officials.

Option A seems to be the logical conclusion. Counter-intuitively, Wald recommended just the opposite, the reinforcement of those areas with the least frequency of bullet holes.

Wald’s profound insight was to focus on the unseen. Taking survivorship bias into account, he grasped that the returning aircraft were the survivors, receiving enemy fire in non-vulnerable areas.

The downed aircraft (which were not part of the data set) were the ones that had received the fatal hits, most likely to the remaining areas. It was those remaining areas (the ones free of bullet holes in the surviving planes) that needed the extra armor plating.

The question is "Which of the following can be concluded from the above?"

The option is C

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