I waited all day in the fond hope that she would change her mind.
我整天等待，痴心地希望她会回心转意。
She waited in the forlorn hope that he would one day come back to her.
她几乎毫无指望地等待他有一天会回到她的身边。
I knocked loudly in the vain hope that someone might answer.
我敲门敲得很响，希望有人应声，却是徒然。
He asked her again in the vain hope that he could persuade her to come.
他又问了她一次，徒然指望着能说服她来。
He pressed on in the hope that a few others would join him. The tactic paid off.
他硬着头皮干下去，希望能有几个人加入进来。这一招奏效了。