Concept: The addition of HBr to an unsymmetrical alkene in the presence of peroxides follows the Anti-Markovnikov rule due to a free radical mechanism, also known as the Kharasch effect.
Step 1: {Identify the structure of propylene.}
Propylene (prop-1-ene) has the chemical formula $\text{CH}_3\text{CH}=\text{CH}_2$.
It is an unsymmetrical alkene with a terminal double bond.
Step 2: {Apply the effect of hydrogen peroxide (H$_2$O$_2$).}
In the presence of peroxides, the addition of HBr proceeds via a radical mechanism.
The bromine radical attacks the less substituted carbon atom to form a more stable secondary radical.
Step 3: {Determine the final product.}
The Bromine atom attaches to the terminal carbon ($\text{C}_1$), and the Hydrogen atom attaches to the middle carbon ($\text{C}_2$).
$$\text{CH}_3\text{CH}=\text{CH}_2 + \text{HBr} \xrightarrow{\text{H}_2\text{O}_2} \text{CH}_3\text{CH}_2\text{CH}_2\text{Br}$$
The resulting product is 1-bromopropane.