What role did a paradox play in the events of macbeth?

The play hinges on the paradoxes you mention because throughout the play, appearances are deceptive which is what "fair is foul. foul is fair" means, i. e., what looks fair is foul and what looks foul is fair. Lady Macbeth tells her husband in Act 1, sc. 5, to put on a false expression to keep people from knowing what he's up to. At the end of the act, in sc. 7, Macbeth himself says the same thing. After the killing of Duncan in Act 2, both Macbeth and Lady Macbeth pretend innocense. In Act 2, sc. 3, Donalbain acknowledges the fact that people are being deceptive - " ... there's daggers in men's smiles." The witches take advantage of Macbeth's paranoia and need for security by giving him a false sense of security with their apparitions. The second and third visions make Macbeth feel invulnerable to attack, but it's all a trick. Even as Malcolm and the others move toward Dunsinane, they are covering their actions with the limbs they've cut down from Birnam woods giving the appearance of moving trees rather than of moving men. In the end, the battle is "lost" by Macbeth and by Scotland in that Duncan is dead, but it is "won" because Macbeth is dead and Malcolm is now king.