Hope /expect/ think
I find there is some confusion in the use of the above three words.
People especially use hope in the place of think.
When we use hope, there is a wish that it should be so.
We hope to reach there before 5 p.m.
( We wish to reach there before 5. p.m. Hopefully, it will happen).
But, think does not have any such connotation.
I think we will reach there before 5. p.m.
( Given the present circumstances, we should be there by 5. p.m. What we wish does not matter. It is just a statement.)
Also, note that there is a slight difference in the usage of expect and think.
Expect is more reliable. You expect certain things because you have either factual proof or previous experience.
We are driving quite fast. The road is very good. There is no traffic. We expect to be there by 5 p.m.
Now go through the three sentences below.
I hope you will do well in the examination. ( I wish it so).
I think you will do well in the examination. ( I am almost sure).
I expect you to do well in the examination. ( I know you. You are a studious person. You have to do well.)
*I hope I have made it clear.