The electrode potential for Bromine is $\pu{+1.07V}$ whereas for Oxygen to be produced it is $\pu{+0.40V}$.
$$\ce{O2 +2H2O + 4e- -> 4OH-}$$
As the electrode potential for bromine is higher, it means bromine should be reduced rather than $\ce{OH-}$ ions.
I'm aware that the concentration affects the electrode potentials, but the question simply states 'an aqueous solution of NaBr' with no reference to concentration whatsoever, so I can only assume standard solutions.
Also, why do we not look at the electrode potentials of other possible reactions at the anode, like;
$$\ce{O2 + 4H+ + 4e– -> 2H2O}~~~~~~~(E=\pu{+1.23V})$$ or
$$\ce{HO2- + H2O + 2e– ->3OH–}~~~~~~(E=+\pu{0.88V})$$ or
$$\ce{H2O2 + 2H+ + 2e– -> 2H2O}~~~~~~~ (E=\pu{+1.77V})$$.
Why are these not viable?