Final answer:
Laertes and Claudius plot Hamlet's death by arranging a poisoned rapier for Laertes to use in a duel and a poisoned drink as a backup plan.
Step-by-step explanation:
The plan that Laertes and Claudius concoct to ensure Hamlet's death is two-fold. First, Claudius persuades Laertes to engage in a fencing match with Hamlet where Laertes' rapier will be dipped in poison, ensuring that even a scratch would be lethal. Secondly, as a backup, Claudius plans to offer Hamlet a poisoned drink during the match.
This vile scheme is the ultimate test of Hamlet's suspicions about Claudius and the depth of Laertes' thirst for revenge after the death of his father, Polonius, and sister, Ophelia. The intricate plan reflects the themes of deceit, treachery, and the lengths to which individuals will go for vengeance which permeate Shakespeare's Hamlet.