The phrase ‘A Shot in the Dark’ means a very general attempt; a wild guess.
You can use ‘a shot in the dark’ to describe a situation that has a small chance of success.
Example of Use: “That was such a difficult question! How did you get it right?” Reply: “I just took a shot in the dark.”
People have been using the term 'shot' in reference to 'attempt' since the mid-19th century; in Joseph Hewlett’s 1841 comedy Peter Priggins, the College Scout, we read: “After waiting for a little while, Ninny made a shot, and went so near the mark.” The origin of the idiom 'a shot in the dark' isn’t specifically known; George Bernard Shaw was first to use it in print in the February, 1895 Saturday Review: “Never did man make a worse shot in the dark.”