Concept:
Addition of HBr to alkenes in presence of peroxides follows the {free radical (anti-Markovnikov) mechanism},
known as the peroxide effect or Kharasch effect.
Step 1: Nature of the intermediate (Statement A)
In styrene (\(\text{Ph–CH=CH}_2\)), radical addition leads to a {benzylic radical},
which is highly stabilised due to resonance.
\[
\Rightarrow \text{Statement A is true.}
\]
Step 2: Role of peroxide (Statement B)
Peroxides decompose to form \(\mathrm{RO^\bullet}\) radicals, which abstract hydrogen from HBr
to generate \(\mathrm{Br^\bullet}\), not \(\mathrm{H^\bullet}\).
\[
\Rightarrow \text{Statement B is false.}
\]
Step 3: Formation of benzene (Statement C)
No rearrangement or elimination produces benzene in this mechanism.
\[
\Rightarrow \text{Statement C is false.}
\]
Step 4: Product distribution (Statement D)
Anti-Markovnikov addition gives \(1\)-bromo-\(2\)-phenylethane as the {major} product,
not a minor one.
\[
\Rightarrow \text{Statement D is false.}
\]
Step 5: Absence of peroxide (Statement E)
Without peroxide, HBr adds via the ionic (Markovnikov) pathway involving a carbocation intermediate.
\[
\Rightarrow \text{Statement E is true.}
\]
Final Conclusion:
\[
\boxed{\text{Statements A and E are correct}}
\]