The correct option is B Recklessness
The words 'prudence' refers to the quality of being careful or cautious.
Option A, absurdity refers to the quality of being ridiculous or wildly unreasonable.
Option B, desperation refers to a state of despair, typically one which results in rash or extreme behaviour.
Option C, detriment refers to the state of being harmed or damaged.
Option D, recklessness refers to the lack of regard for the danger or consequences of one's actions.
Thus, according to the meaning, the word 'recklessness' is the farthest in meaning from the word 'prudence'.