Faith is defined as confidence or trust in a person or thing or belief not based on proof.
Hope is defined as feeling of optimism or a desire that something will happen.
Now faith is the assurance of things hoped for, the conviction of things not seen.
Christians have faith that:
The Bible is the Holy Word of God.
Jesus Christ died for our sins.
Jesus rose from the dead.
We will spend eternity with God.
A correlation between Hope and Faith can be summarized by the following statement - it can be difficult in any situation to have Hope if you don't currently have Faith. For instance if you have Faith that a doctor is qualified to treat an ailment you likely will have more Hope in a positive outcome.
11 For I know the plans I have for you, declares the Lord, plans for welfare and not for evil, to give you a future and a hope.
Along the journey of life we will all have difficult times just as we will all have joyous times. During our life it is important to have a strong and personal relationship with Jesus Christ.
I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me.
May the God of hope fill you with all joy and peace in believing, so that by the power of the Holy Spirit you may abound in hope.
For this very reason, make every effort to supplement your faith with virtue, and virtue with knowledge, and knowledge with self-control, and self-control with steadfastness, and steadfastness with godliness, and godliness with brotherly affection, and brotherly affection with love. For if these qualities are yours and are increasing, they keep you from being ineffective or unfruitful in the knowledge of our Lord Jesus Christ.