A biblical example of fate are the Israelites. These people are the chosen people of God. They were enslaved by the Egyptians and sent to foreign countries, but were ultimately led to the promise land. God let these people be enslaved and live a hard life but this may have been to develop them as Christians.
I think Shakespeare believed in fate and free will. The best example which leads me to believe this is the witches. The witches tell him that he will be thane of Cawdor and Glamis. They know his predestination and are revealing it to him this way.
First Witch
All hail, Macbeth! hail to thee, thane of Glamis!
Second Witch
All hail, Macbeth, hail to thee, thane of Cawdor!
Third Witch
All hail, Macbeth, thou shalt be king hereafter!
When Macbeth heard this from the witches he tries to question them and learn more about this intriguing destination. He is confused because he is not heir to Cawdor, Duncan is the king and his sons are his successors. After them, he is next in line. Macbeth tells Lady Macbeth about the prophecy. Lady Macbeth plots the idea to murder Duncan and tries to push the intentions into her husbands head. He, however, does not initially agree with the idea, for he and Duncan are close friends. Ultimately, Lady Macbeth persuades Macbeth to commit the crime with her and they kill Duncan. It is by fate that Macbeth becomes heir to the throne because after he kills the guards, Malcolm and Donalbain are still in the way of the goal. Macbeth does not have to try and kill them though, because they flee to Ireland and England in fear that they would be tried to murder as well. Thus, by this action, Macbeth becomes the king. The prophecy of the witches becomes true. But how much of this was determined by free will? Each action was a choice that he made but the destination was already predetermined by God.
Wyrd means fate. Shakespeare has a common trend of fate in the play and shows how it can affect the actions of the characters. Through this concept of wyrd, the witches prophecy becomes reality and, in my opinion, shapes Macbeth and Lady Macbeth's actions to commit the deed.