The reaction of an alkene with #"HBr"# in the presence of peroxides is a free radical reaction.
The product is the "anti-Markovnikov" product, in which the #"H"# atom adds to the carbon atom with fewer hydrogen atoms.
The overall reaction is
#"CH"_3"CH"_2"C"("CH"_3)"=CH"_2 +color(red)("HBr") stackrelcolor(blue)("ROOR", Δcolor(white)(mm))(→) "CH"_3"CH"_2"C"color(red)("H")("CH"_3)"-CH"_2color(red)("Br")#
The mechanism
(a) Initiation
#"RO-OR" color(white)(l)stackrelcolor(blue)(Δcolor(white)(mm))(→) "RO· + ·OR"#
#"RO· + H-Br → ROH + ·Br"#
(b) Propagation
#"CH"_3"CH"_2"C"("CH"_3)"=CH"_2 + "·Br" → "CH"_3"CH"_2stackrelcolor(blue)(bb.)("C")("CH"_3)"-CH"_2"Br"#
#"CH"_3"CH"_2stackrelcolor(blue)(bb.)("C")("CH"_3)"-CH"_2"Br" + "HBr" → "CH"_3"CH"_2"C"color(red)("H")("CH"_3)"-CH"_2color(red)("Br") + "·Br"#
(c) Termination
#"R· + ·R → R-R"#
#"R· + ·Br → RBr"#
#"Br· + ·Br → Br-Br"#
