Step 1: Understand a 1:3 electrolyte.
In water, the part inside the square brackets stays together as one complex ion, while the ions outside the brackets break free. A 1:3 electrolyte gives a total of four ions: one complex ion and three counter ions (or one ion of charge that balances three of the other).
Step 2: Test option 1, \([Co(NH_3)_3(NO_2)_3]\).
Nothing sits outside the brackets, so it does not ionise. This is a non-electrolyte, not 1:3.
Step 3: Test option 2, \([CoCl_2(NH_3)_4]Cl\).
Only one \(Cl^-\) is outside, giving one complex cation and one chloride. That is a 1:1 electrolyte.
Step 4: Test option 3, \([CoCl(NH_3)_5]Cl_2\).
Two \(Cl^-\) are outside, giving one complex cation and two chlorides. That is a 1:2 electrolyte.
Step 5: Test option 4, \([Co(NH_3)_6]Cl_3\).
Three \(Cl^-\) are outside: \[ [Co(NH_3)_6]Cl_3 \rightarrow [Co(NH_3)_6]^{3+} + 3Cl^- \] One cation and three anions: this is the 1:3 electrolyte.
Step 6: State the answer.
The 1:3 electrolyte is \([Co(NH_3)_6]Cl_3\), option 4.
\[ \boxed{[Co(NH_3)_6]Cl_3} \]