<u> B) It had been a most unpleasant coincidence that the power outage had come when we had guests staying over; the entire house was full.</u>
This is the correct answer because the semicolon is carrying out its function here: to join two independent clauses that are related to each other.
A, C and D are wrong because they all have conjunction following the semicolon: "and" and "so". And semicolons aren't used with conjunctions, as for they both perform the same function: to link two independent clauses. So when trying to connect two independent clauses, we can either use a semicolon or conjunction, not both at the same time.
