Final answer:
A common interpretation from Shakespeare's 'Hamlet' concerning his belief in fate is illustrated by his line to Horatio, 'There's a divinity that shapes our ends.'
Step-by-step explanation:
The quote that demonstrates Hamlet's belief in fate is not explicitly provided in the given excerpts. However, a common interpretation from Shakespeare's Hamlet is reflected in Hamlet's words in Act V, Scene 2, where he says to Horatio, "There's a divinity that shapes our ends, Rough-hew them how we will." This line supports the notion that Hamlet believes in a higher power or divinity that ultimately shapes the destiny of individuals, despite their own actions or intentions.
In the passages provided, Hamlet engages in a dialogue with Polonius and Horatio over the existence of ghosts and the nature of man's reason, which suggests an analysis of the supernatural vs. rational thought, rather than a direct statement on fate. It is worth noting that throughout the play, Hamlet often contemplates the intersection of free will, destiny, and the choices one makes within the confines of fate.