What is an example of fate or free will in Act Four of Macbeth?

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In the first scene of Act Four, the witches conjure up three spirits that make three separate predictions about Macbeth's future. The first, a disembodied head, warns him to "beware the Thane of Fife," i.e., Macduff. The second, a bloody child, tells Macbeth to

Be bloody, bold, and resolute; laugh to 
scorn The power of man, for none of woman born 
Shall harm Macbeth. 

The third apparition, a "child crowned, with a tree in his hand" assures the king that

Macbeth shall never vanquish'd be until 
Great Birnam Wood to high Dunsinane Hill 
Shall come against him. 

These prophecies fill Macbeth with confidence, suggesting that he is fated to be safe against all opponents. But then he sees a final vision, one of the murdered Banquo and seven of his descendents, all of whom wear the crown of Scotland. This suggests that Banquo's line will be kings, not Macbeth's which deeply disturbs him. Still, takes solace in the prophecies. His confidence is short-lived, however, as he hears that the army approaching his castle disguises itself with limbs from the trees from Birnam, giving the appearance of a forest marching on the Dunsinane. Then, just before his climactic battle with Macduff, he discovers that the Thane of Fife was not, strictly speaking, born of woman, but taken by Caesarian section. His fate, forecast in Act Four, comes true, but not in the way he expected.