The fermi level of an intrinsic semiconductor is pinned at the center of the band-gap. The probability of occupation of the highest electronic state in the valence band at room temperature can be explained as follows:

1. Fermi Level in an Intrinsic Semiconductor:
- In an intrinsic semiconductor, the number of electrons in the conduction band is equal to the number of holes in the valence band.
- The Fermi level represents the energy level at which there is a 50% probability of occupation by an electron.
- In an intrinsic semiconductor, the Fermi level is located at the center of the band-gap due to the equal number of electrons and holes.

2. Valence Band:
- The valence band is the highest energy band that is fully occupied by electrons at absolute zero temperature (0 Kelvin).
- At room temperature, some electrons in the valence band gain enough thermal energy to move to the conduction band, creating holes in the valence band.

3. Probability of Occupation:
- At room temperature, some electrons in the valence band gain enough thermal energy to move to the conduction band, creating holes in the valence band.
- The probability of occupation of the highest electronic state in the valence band refers to the likelihood of this state being filled by an electron.
- Since the Fermi level is pinned at the center of the band-gap, the highest electronic state in the valence band is closer in energy to the Fermi level than the lowest energy state in the conduction band.
- At room temperature, the probability of occupation of the highest electronic state in the valence band is approximately half (50%) because the Fermi level is equidistant from the highest electronic state in the valence band and the lowest energy state in the conduction band.

Therefore, the correct answer is option 'C' - half, as the probability of occupation of the highest electronic state in the valence band at room temperature is approximately 50%.