Probability Paradoxes & Puzzles Calculators
Explore famous probability problems where the correct answer contradicts first intuition.
Probability paradoxes are problems where a natural first answer turns out to be wrong. They are useful because each one exposes a specific reasoning trap, such as ignoring how information was obtained or treating unequal cases as equally likely.
The tools in this category let you change the parameters of a classic puzzle and see how the result responds, which is usually the fastest way to understand why the surprising answer is correct.
Calculators in this category
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Key concepts
- Conditioning on information
- Many paradoxes hinge on what a person knows and how they came to know it. The same event can have different probabilities depending on the process that revealed it.
- Equally likely outcomes
- Counting outcomes only works when each outcome has the same probability. Several classic puzzles go wrong by treating unequal cases as equal.
- Base rates
- The overall frequency of a condition in a population. Ignoring it is the source of the false positive paradox.