Step 1: Understanding ozone's structure.
The structure of the ozone molecule (\(O_3\)) is bent, with one oxygen having a double bond and the other having a single bond to the central oxygen atom.
The central oxygen has a formal charge of 0, and one of the terminal oxygens has a formal charge of 0, while the other has a formal charge of \(-1\).
Step 2: Formal charge calculation.
For the terminal oxygens, the formal charge is calculated as:
Formal charge = \( \text{Valence electrons} - \text{Bonding electrons} - \frac{\text{Lone pair electrons}}{2} \).
For the oxygen with a single bond and a lone pair, the formal charge is \(-1\), while for the oxygen with a double bond, the formal charge is \(0\).
Step 3: Conclusion.
The correct formal charges on the terminal oxygens of the ozone molecule are \(0\) and \(-1\), which corresponds to option (4).