A shot/stab in the dark
Definition 1 of 1
Pro Tip 1/3Guesswork
Used when you rely on instinct without facts to support your choice. 
Without any clues, my answer was just a shot in the dark.
Pro Tip 2/3Informal
Common in casual conversation; may not be suitable for formal writing or speeches. 
Picking a career can sometimes feel like a shot in the dark.
Pro Tip 3/3No Expectations
Implies you don't really expect to be correct due to the randomness of your attempt. 
I took a stab in the dark when choosing the name for our team.