B — the two drives. Same model (shared manufacturing defects and firmware bugs), same enclosure (shared vibration and temperature), same power rail (shared surges). These aren’t two independent 3% dice; they share common causes, and a common cause is exactly what makes learning about one event move your belief about the other. When drive 1 dies, P(drive 2 dies this year) is no longer 3% — the ambient temperature, the power event, or the bad firmware batch that killed drive 1 is still right there. The honest calculation is the multiplication rule from last lesson: P(both) = P(second | first) · P(first), and P(second | first) can be ten times the marginal rate. Storage engineers learned this empirically: correlated drive failure is why RAID arrays die during the rebuild, and why serious systems mix models, batches, and racks.
The other three are the textbook-legal cases: separate coins, separate dice, and a coin plus a die genuinely share nothing — learning one outcome tells you nothing about the other.
Why this error matters beyond hardware. In 1999, Sally Clark was convicted of murdering her two infant sons after an expert testified that two natural crib deaths in one family had probability 1 in 73 million — computed as (1 in 8,543)². Squaring assumes the two deaths were independent. But siblings share genetics and environment — precisely the common-cause structure of the drives. Real family data shows a second crib death is far more likely than the marginal rate. The conviction was eventually overturned; statisticians cite the case as the canonical independence abuse. The same error, pointed the other way, is double-counting evidence: two alerts from the same broken metric, two “independent” reviewers who read each other’s comments, two models trained on the same skewed data. Agreeing copies are not multiplying evidence.
The pitfall in one line: independence is an assumption you must argue for (what could the common cause be? did the sources actually see different things?), never a default you fall back on because the multiplication is easier.
Where this goes: near the top of this track sits the practice of compounding evidence — combining two test results, two witnesses, two log lines. The condition that makes compounding legitimate is a refinement called conditional independence, and you now have every concept it’s built from.