What does it mean to "hazard 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”.
hazard verb [trans.]
venture to say (something): he hazarded a guess.
It's like “make a guess”, really. Maybe a bit more uncertain, even.
In addition to meaning, I should say that it is very commonly used:
