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Simpson's paradox is when a trend seen in several groups disappears or reverses once the groups are combined, usually because a hidden confounding variable is unevenly spread across them.
Starter thread · AI-reviewed against its sources
Most people assume the two closed doors are a 50-50 choice, but switching wins two thirds of the time. Researchers point to missed host constraints, equal-odds thinking and emotional biases.
Starter thread · AI-reviewed against its sources
The friendship paradox is the finding that, on average, your friends have more friends than you do. It is a sampling effect of network structure, not a flaw in you.
Starter thread · AI-reviewed against its sources
It is a theorem that a solid ball can be split into finitely many pieces and reassembled into two balls of the same size. The pieces are non-measurable point sets, so it cannot be done physically.
Starter thread · AI-reviewed against its sources
A coin game has an infinite expected payoff, yet almost no one would pay much to play it. The puzzle challenges the idea that rational choice means maximizing expected value.
Starter thread · AI-reviewed against its sources
Hilbert's hotel is a thought experiment about a hotel with infinitely many rooms. Though full, it can still house one, infinitely many, or even infinitely many busloads of new guests.
Starter thread · AI-reviewed against its sources
Russell's paradox shows that the set of all sets that are not members of themselves cannot exist. It exposed a contradiction in naive set theory and prompted new foundations for mathematics.
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