* The difference between those four is quite subtle.
Wahrscheinlich and vermutlich
mean that the action seems to be quite probably. Vielleicht
and möglicherweise
mean that the probability is a bit smaller than with
wahrscheinlich and vermutlich.
Compare these phrases
Vielleicht
hat er es verloren.
Maybe he
has lost it.
Wahrscheinlich
hat er es verloren.
Probably he has lost
it.
Vermutlich
hat er es verloren.
Presumably he has lost
it.
Vielleicht
weiß er es.
Maybe he knows.
Wahrscheinlich
weiß er es.
Probably he knows.
In the following sentences you'll
find the difference more clearly.
Wahrscheinlich
weiß er es, aber er will es uns nicht sagen.
Probably
he knows, but he doesn't want to tell us.
Vielleicht
weiß er es, aber er will es uns nicht sagen.
Maybe he knows, but he
doesn't want to tell us.
In the first sentence there is little doubt that "he
knows". In the second sentence the doubt is stronger.
However the difference is subtle.