Explain

Intuition

The conclusion is often counterintuitive to people because humans naturally look for patterns. For instance, if you saw two cells hit twice but their neighbor was not hit at all, you might think "they are clearly targeting those two cells!"

However, mathematical reasoning like the Poisson distribution allows us to test if "patterns" in random events (bomb hits landing in the area) actually mean something or are simply the result of chance. In the long run, even a completely random process creates clumps or empty areas—this is called the "law of true randomness".

The incredibly close match between the mathematical predictions (the "expected" row) and reality (the "observed" row) shows us precisely that these "clumps" of hits were just a statistical inevitability. The Poisson model tells us exactly what randomness looks like. The Germans weren't highly accurate—they were just dropping enough bombs that, statistically, somewhere had to get hit 3 or 4 times.

To summarize the intuition: randomness isn't uniform. A perfectly even spacing of hits would be much more suspicious. Finding clusters of hits does not prove intention; it instead might be the very definition of random chance unfolding over a large area.