Identify the compound sentence.

1) Last summer, we decided to drive to the beach.
2) Because it had been sunny all week, we did not bring umbrellas.
3) The rain began to fall, but we did not want to leave.
4) While it rained on the beach, we swam in the ocean.
This one I think is #3, but I am not 100% sure.

You're absolutely right! The third sentence is the only that has two clauses that can each stand alone.

You are correct! The compound sentence is number 3: "The rain began to fall, but we did not want to leave."

A compound sentence is a sentence that consists of two or more independent clauses (complete thoughts) joined together by a coordinating conjunction (such as "and," "but," or "or") or a semicolon. In this case, the coordinating conjunction "but" is used to join the two independent clauses "The rain began to fall" and "we did not want to leave."