Maybe Possible

Possible is a synonym of maybe.
As adjectives the difference between possible and maybe is that possible is (usually|not comparable) able but not certain to happen; not impossible while maybe is possible; uncertain.
As nouns the difference between possible and maybe is that possible is a possible one while maybe is (informal) something that is possibly true.

As a adverb maybe is .

https://wikidiff.com/possible/maybe

Confused ?

Suggest something that maybe is possible. 

If evidence exists, feel free to present.

Of course … stating that "something" maybe is possible makes no sense at all.

However, we can ignore the hyperbole and get to it.  We are looking for events (though highly unlikely) maybe are possible.

Proofs are welcome, except mathematical ones. 

OK. Let's get the ball rolling.

It is maybe possible Caruana will win the WC.

Evidence ?

A Damn fine chess player. 

Why no mathematical proofs?

Because mathematics is abstract thought.