Step 1: Understanding the Concept
Without peroxide, HBr adds by the Markovnikov rule (ionic path). With peroxide it adds by the anti-Markovnikov rule (free radical path).
Step 2: When products differ
The two products are different only when the alkene is unsymmetrical.
Step 3: Check the alkenes
2-Butene, \(\text{CH}_{3}\text{CH}=\text{CHCH}_{3}\), is symmetrical. Br on either alkene carbon gives 2-bromobutane in both cases.
1-Butene, propene and 2-methylpropene are unsymmetrical, so they give different products.
Final Answer:
2-Butene gives the same product in both conditions.
\[ \boxed{\text{(A) }\text{2-butene}} \]