Past tense of 'hazard'; exposed something to risk, danger, or loss; took a chance on something uncertain.
From 'hazard' (Old French origin) plus past tense suffix '-ed,' preserving the concept of risking or gambling introduced by the medieval noun.
When you've 'hazarded a guess,' you're etymologically speaking making the same kind of risky bet that medieval people made with dice games—language preserves ancient gambling culture in our everyday speech.
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