Question

Data on planes returning from bombing missions was used to study 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?

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

Hint:

This is a classic example of \emph{survivorship bias}. When analyzing success/failure data, always ask: "What data am I missing?" In this case, the missing data (planes that did not return) revealed the true vulnerabilities.

Answer 1

The Correct Option is C

Step 1: Understand the context of the data.
The analysis was conducted on planes that returned from missions. These planes had visible bullet damage in certain areas. However, planes that did not return (those shot down) could not be studied. 

Step 2: Apply survivorship bias reasoning.
If planes return safely despite heavy damage in some parts, this means those parts can take hits without causing the plane to be destroyed. In contrast, the parts that showed little or no damage in surviving planes may actually be critical vulnerabilities—because if those parts had been hit, the planes would not have made it back. 

Step 3: Evaluate the options.
- (a) Incorrect. Reinforcing the most frequently hit areas is unnecessary since planes survived hits there.
- (b) Incorrect. A clear conclusion can be drawn by accounting for survivorship bias, so "no conclusion" is wrong.
- (c) Correct. The parts with least visible damage in returning planes are the most critical and must be reinforced. This is the well-known insight from Abraham Wald's WWII aircraft study.
- (d) Incorrect. Reinforcing all areas is inefficient due to weight constraints, which the passage highlights. \[ \Rightarrow~\boxed{(c)~\text{The least damaged areas must be reinforced, since hits there downed the missing planes.}} \]