In a semiconductor consider the energy level lying $0\mathrm{.}11eV$ below Fermi level. Find:

$($a$)$ The probability of this level being occupied by the electron at room temperature.

$($b$)$ The probability of this level not being occupied by the electron at room temperature.

$($c$)$ The probability of this level not being occupied by the electron at $500K.$

$($d$)$ Discuss your result!