Also the probability of an event E not occurring is P(E') = 1 - P(E)

Lets provide a breakdown of the events here:
Total Students = 80

P(Geo) = $\frac{ 24}{80 }$

P(Bio) = $\frac{ 40}{80 }$

P(Both) = $\frac{ 20}{80 }$

P(Geo or Bio) = P(Geo) + P(Bio) - P(Both)

$\implies$ P(Geo or Bio) = $\frac{ 24}{80 } + \frac{ 40}{80 } - \frac{ 20}{80 }$

$\implies$ P(Geo or Bio) = $\frac{ 24 + 40 - 20}{80} = \frac{ 44}{80} = \frac{ 11 }{ 20 } = 0.55$

The question requires us to pick a student who has not enrolled in either of these courses:

$\implies$ P(Both') = 1 - P(Both) = 1 - 0.55 = 0.45

Thus the answer is Option C