What one word could describe the central idea of the
sentences?
worry
enjoyment
friendship
fear

In the given sentence above, there are two independent clauses and no subordinate clause. the independent clauses are, "jean prepared for rain by packing an umbrella" and "the sun ended up coming out". these two have a subject and a predicate, and conveys  a complete thought. the sentence given is an example of a compound sentence. two independent clauses connected by a coordinating conjunction "but".