wild guess

take a wild guess — ответить наугад
(wild guess — домыслы; смутные догадки)

Example: A proud father recently told me of quizzing his kids about scurvy. And while his young daughter gamely took a wild guess, his crafty teenage son ducked into the next room to google it, quickly emerging to give the correct answer that the disease that killed so many centuries ago is caused by a deficiency of vitamin C.
Example:

Related vocabulary:
[наугад]

Cf.:
an educated guess/ an informed guess
a guess that is likely to be right because it is based on knowledge of the situation