Step 1: Spot the key reagent: a peroxide is present, so this is anti-Markovnikov (Kharasch) addition, not the ordinary Markovnikov addition.
Step 2: Markovnikov's rule says H goes to the carbon with more H atoms; the peroxide effect reverses this, so here H adds to the more substituted carbon and Br to the less substituted (terminal) carbon.
Step 3: The alkene \(CH_3CH_2CH=CH_2\) (but-1-ene) therefore takes Br on carbon 1, the CH2 end.
Step 4: The product is 1-bromobutane, \(CH_3-CH_2-CH_2-CH_2-Br\). The peroxide effect is observed only with HBr, not with HCl or HI.
\[\boxed{CH_3-CH_2-CH_2-CH_2-Br}\]