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    The paradox reveals that 'geometric validity' alone canno... — Carmelics
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    Supports→Bertrand's chord paradox shows that three geometrically valid but non-equivalent equipossibility partitions yield probabilities of 1/3, 1/4, and 1/2 for the same event, proving internal inconsistency.

    The paradox reveals that 'geometric validity' alone cannot determine probability—something non-geometric must specify which partition reflects reality.

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