希望渺茫
a long shot
(1) shot “尝试（尤指做困难的事）”
(2) a long shot “成功希望不大的尝试，希望渺茫”
英语解释为an attempt or a guess that is not likely to be successful but is worth trying。
例
It was a long shot anyway.
总之，希望渺茫。
It's a long shot, but it just might work.
希望不大，但也许能行。
Listen, I know it's a long shot, but by any chance, did she find that funny?
我知道机会渺茫，可是她觉得这件事好笑吗？《老友记》
其他
(1) give it a shot “尝试一下，试试”
例
At least let me give it a shot.
至少让我试试。
If neither of us is with anybody in 10 years, how about you and me give it a shot?
如果十年以后我们还都是单身，我们俩试试行吗？
没 报 太大希望
not have high hopes
(1) have high/great hopes “抱有很大希望”
英语解释为be very confident about it。
(2) have high/great hopes for sb./sth. “对......抱有很大希望”
英语解释为to be confident that someone or something will be successful。
(3) not have high/great hopes “没报太大希望”
例
She has high hopes of winning.
她对成功抱有很大希望。
I've seen the kid fall down on that moving sidewalk at the airport, so I didn'thave high hopes.
那孩子连在机场的自动人行道上都能摔跤，所以我没抱太大希望。