Would an Elizabethan audience have believed Macbeth was fated to murder King Duncan because of the witches' prophecy?

Actually, Shakespeare's audience would not have liked the idea that fate is ultimately in control of one's destiny. Unlike the ancient Greek audience, who would have been much more comfortable with the idea of fate, Elizabethan audiences wanted to think of themselves as being in control of their lives. If one's choices are sealed by fate, then one cannot actually make any decisions other than the ones fate already determined; the individual really has no control over anything in his or her life. He or she is simply the pawn of fate, subject to whatever has already been predetermined.  Shakespeare's audience very much wanted to believe their choices had meaning and impact in their lives, that they were ultimately in control of their decisions and were not influenced by some uncontrollable, unknowable force. Thus, they would not have wanted to believe Macbeth had to kill Duncan; they would have preferred to believe that Macbeth simply made his own terrible decision.