  The role played by the mutual information of subsystems on the Page curve is
explored in this paper. With the total system consisting of the black hole and
radiation, together with the inclusion of island, we observe that the vanishing
of mutual information between $B_+$ and $B_-$ which in turn means the
disconnected phase of the entanglement wedge corresponding to $B_+\cup B_-$,
yields a time scale of the order of scrambling time. This results in a time
independent expression for the fine grained entropy of Hawking radiation
consistent with the correct Page curve. We also find corrections to this
entropy and Page time which are logarithmic and inverse power law in form.
