Fate: This is when you have no choice in what happens in your life. Those choices are left to a higher or a supernatural power.
Chance: This is when the events in your life happen because of luck. There really is no explanation, they just happen because they do.
Now that I have established my definitions of these two similar words I can get into why I believe the events in Macbeth's life are fate. In the beginning of the story we have the witches telling Macbeth what is going to happen with his life. When a witch tells you what is going to happen you better listen up and accept it. When has a witch ever been wrong in a story? Never. Due to this Macbeth has no choice in what his life was about to become, it is what it is. The proof of this is when Lady Macbeth tries to take over Macbeth's role in killing Duncan. Lady Macbeth claims she couldn't do it because Duncan looked too much like her father. Is that true or is it fate because the witches said so. Lady Macbeth had so much confidence and power in herself and then she couldn't kill Duncan. Coincidence? I think not. Shakespeare has chosen to have Macbeth's life be based on fate. Whether Shakespeare actually believed in fate or chance is unclear as I think it is wrong to base his opinion off of his book.
Personally I don't believe in fate or chance. I believe everything happens for a reason. Yes, some people call that fate, but I believe that reason is who ever is making the decisions. That everything happens for a reason, but you can control that reason and your choices. I know that's confusing, but I don't know a better of explaining it.
Fate vs. destiny vs. chance vs. luck. My thought process is you make your own decisions and you shouldn't blame them on anything else except yourself because you are the one that made them.