Analyze the statements below: I. In “You must buy a ticket to enter the m...

Analyze the statements below:

I. In “You must buy a ticket to enter the museum”, the word “must” indicates an obligation.
II. In “You don’t have to go to the meeting if you’re busy”, the use of “don’t have to” indicates a prohibition.
III. In “You must read this, I’m sure you’ll find it interesting”, “must” indicates a strong recommendation, but not an obligation.

Which ones are correct?