I know it's an idiomatic synonym for "make a guess" or "take a guess," but what is the underlying basis for the phrase? Is "hazarding a guess" more dangerous than "taking a guess?"
The word “hazard” is (probably) from an arabic word meaning “dice”, and came to English through French where it originally meant a game of dice and then more generally chance, randomness. The word further evolved in English to mean risk, then danger. I'll hazard the guess that “hazard a guess” is an idiom that retains the older meaning of “taking a chance on a guess”.