“Possibility”, in English, is far more restricted in use than its German counterpart, “Möglichkeit”. Grammatically, “possibility to” does not exist; instead, it colligates with “of” and “that”:
There’s only a slight possibility of something going wrong with that experiment.
Officials could not exclude the possibility that an insider leaked information.
Semantically, the usage above refers to the probability of something statistically happening (ie. 5% chance, 50-50). In its other uses, “Möglichkeit” is best translated by “opportunity”:
We just missed the opportunity to view their new state-of-the-art laboratory.
They will have a great opportunity to work for an international commodities trader this summer.
an equal opportunity employer (Chancengleichheit)