Final answer:
In Shakespeare's 'Hamlet,' Queen Gertrude drinks to Hamlet's success after his second hit in the fencing match, unaware of the poison, as King Claudius's failure to intervene would reveal his murderous intent.
Step-by-step explanation:
In the context of William Shakespeare's Hamlet, after Hamlet scores his second hit in the fencing match, it is his mother, Queen Gertrude, who drinks to his success. She does this in spite of the fact that the King had tried to dissuade her, hinting at the poisoned nature of the drink.
The King, Claudius, does not intervene when Gertrude drinks because doing so would expose his plot to murder Hamlet. Not only is this moment critical to the play's climax, revealing the depths of Claudius's treachery, but it also serves to bring about the tragic end that engulfs the royal family.
In Act 2 of Hamlet, Hamlet chooses not to drink and implies that drinking can provoke three things. After his second hit, it is Lady Macbeth who drinks to him.
The reason why the king does not intervene is not directly stated in the given information, so it can be speculated that he may not intervene because he is either unaware of the situation or he does not see it as significant.