Question

I'm sure she (pass) the exam

Answer 1

I'm sure she'll pass the exam.

Answer 2

I’m sure she will pass the exam.  

Explanation:  

Modals are special irregular words that add more meaning to the verb. They are not like the normal verbs like eat and sleep as they add the speaker’s intentions and emotions to the main verb. Examples of modal verbs are will, shall, must, can and could.

Here pass is the actual verb. The speaker here expresses a possibility and thinks that she can or may pass the exam. So 'will' is used here as a modal to add more information to the main verb pass.