shot in the dark

a shot in the dark
a stab in the dark (an attempt to guess something without having any facts or definite ideas; a random guess at an answer you have no idea about) — догадка или попытка, сделанная наобум, пальцем в небо; попытка вслепую; предположение, высказанное наугад; попытка без особой надежды на успех; нечто, сделанное от балды (без предварительных размышлений или подготовки); навскидку

Example 1: My answer to the last question was a complete shot in the dark. — Я ответил на последний вопрос наугад.

Example 2: The whole theory is a shot in the dark - no-one will ever take us seriously. (CIDI)

Example 3: When I applied for the scholarship, it was just a shot in the dark – I had no idea how important and competitive it was. (CIDI)

[wide of the mark]