Answer
$ P(E) = 0.824 $
Work Step by Step
The energy of donor state
$E = 1.11 eV - 0.15 eV$
$E = 0.96 eV$
The Fermi Energy
$E_F = 1.11 eV - 0.11 eV$
$E_F = 1.00 eV$
Solve for probability
$ P(E) = \frac{1}{e^{E_1 - E_F/kT} + 1}$
$ P(E) = \frac{1}{e^{(0.96 eV) - ( 1.00 eV)/0.02586eV} + 1}$
$ P(E) = 0.824 $
