You say hopefully when mentioning something that you hope will happen. Some careful speakers of English think that this use of hopefully is not correct, but it is very frequently used.
Hopefully, you won't have any problems after reading this.
但愿你读完这个后就不会有什么问题了。
If you do something hopefully, you do it in the belief that something that you want to happen will happen.
'Am I welcome?' He smiled hopefully, leaning on the door.
“欢迎我吗?”他倚着门,满怀希望地笑着问道。