The first to die is Polonius, chief counselor to Claudius. Polonius dies when Hamlet stabs him through a wall hanging. Some may argue that it is Polonius's fault that he dies, saying that if he would not have been eavesdropping then Hamlet would have never killed him. However, others may argue that Polonius's death is Gertrude's fault for screaming for help. But it is Hamlet's fault for not believing the ghost. When Hamlet kills Polonius it is one of the few times that he actually does act on impulse. "Is it the king?" (3.4.28) asks Hamlet. Unfortunately, it is not the king and Hamlet has killed an innocent man. The death of Polonius could have been prevented if Hamlet would not have questioned what the ghost told him. But Hamlet wants to make sure that what the ghost told him is true before he kills Claudius. Hamlet gets some players to put on a play for the king and queen. The play, called The Murder of Gonzago involves a scene in which a king is murdered by someone pouring poison in his ear. Hamlet is sure that what the ghost has told him is true when he sees Claudius's reaction to the play. But Hamlet does not kill him right away and because of this Polonius gets killed. Polonius never would have been behind the arras if Hamlet would have killed Claudius as soon as he was sure of his guilt.
Ophelia's death could have also been prevented if Hamlet would have killed Claudius right away. Ophelia becomes mad after her father's death. Whether or not she was mad because her father died, or because the man she loved (Hamlet) is the one who killed her father is uncertain. Ophelia just walks around the castle singing tunes that do not make any sense in an almost trance-like state. Opelia falls into the stream when the branch she is sitting on breaks. She was weaving garlands and hanging them from the tree. Ophelia dies when Hamlet is away but her death is still his fault.