Option is often used synonymously with possibility, referring to something that may or may not happen. This is fine, until it comes to legal English, where each word may have specific meanings. If you are not familiar with those meanings, your mistake may lead to significant consequences.
Let's start with the easier one, possibility. This is basically a "binary", meaning that something will either take place or not.
Option is choice that one may make or that the law may provide. It is a possibility to elect something that you have the right to.
As nouns the difference between possibility and option is that possibility refers to something happening or not happening, while option refers to taking advantage of is one of the choices which can be made.
