Answer
$ P(E) = 1.5 \times 10^{-6}$
Work Step by Step
The formula of probability
$ P(E) = \frac{1}{e^{E_1 - E_F/kT} + 1}$
Where
$k = 8.62 \times 10^{-5} eV/K$
E at the bottom of conduction band = 0.67 eV
For Germanium,
$E_F=0.335 \space eV$
$T = 290 K$
$ P(E) = \frac{1}{e^{(0.67 eV - 0.335 eV)/(8.62 \times 10^{-5} eV/K)(290 K)} + 1}$
$ P(E) = 1.5 \times 10^{-6}$
