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: The data only comes from planes that returned; planes hit in truly critical spots never made it back and are missing from the sample.

Step 2: Areas showing heavy damage on returning planes are proven survivable, since those planes still made it home.

Step 3: Areas showing little or no damage on returning planes are the actual danger zones, since a hit there likely brought the plane down.
\[ \boxed{\text{Reinforce the least-damaged areas}} \]