Final answer:
Coincidence can play a role in Act III of a play by bringing characters together and advancing the plot. The importance of the coincidence in the play's narrative is that it creates unexpected connections between characters. The believability of the coincidence depends on whether it arises from the characters' actions and choices.
Step-by-step explanation:
ACT III of a play often contains important events and conflicts that propel the plot forward, and coincedences can play a role in these developments. In the play's narrative, coincidences can create unexpected connections between characters and contribute to the tension and drama of the story. The believability of a coincidence depends on whether it is a natural result of the characters' actions and choices. In this case, if the coincidence is a plausible outcome of the characters' decisions, it can be seen as believable within the context of the play.