Suppose the sentence p is possible, and -p is impossible.
Is the disjunction p v -p necessary?
Formal tautologies are always logically necessary. Standard FOL has p v -p as a formal tautology, hence it is necessary regardless of whether p is necessary or possible. This breaks down if you consider alternative logics that don't have the Law of Excluded Middle as a tautology.
p
can be possible without being necessary.