We use expect to say that we believe that something will happen. We use expect in the following main patterns: expect + object/ to (infinitive)/ that (clause)/ object + to (infinitive)
i.e. We expected that the guest house would have much better rooms.
i.e. The company expects her to be early.
We use hope when we do not know whether something will happen or not but we want it to happen. We use hope in the following patterns: hope + to (infinitive)/ that (clause)/ for
i.e. We’ve already got two boys so we’re hoping for a girl.
i.e. I hope that your sister recovers quickly from the operation.