A study followed $800$ patients diagnosed with a certain medical condition and found that $25\%$ of them experienced symptom Y within the first year. Based on this study, which of the following statements must be true?

I. Among all patients diagnosed with this condition, exactly $25\%$ experience symptom Y within the first year.
II. If a second study follows another $800$ patients with the same condition, exactly $25\%$ will experience symptom Y within the first year.
III. If a study follows $800$ patients with a related, but different, medical condition, exactly $25\%$ will experience symptom Y within the first year.