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This is a difficult question because the lines between fate and chance are blurred, it seems to me, in Sophocles' Oedipus the King. The word "fate" is related to the Greek word phemi (pronounced "fay-me"), which denotes something spoken. Thus, when we think of fate in Sophocles' play, we should look to the things spoken by the gods, namely Apollo's oracle at Delphi. This is what is fated to happen to Oedipus:
But when he spoke he uttered monstrous things,
strange terrors and horrific miseries—
it was my fate to defile my mother’s bed,
to bring forth to men a human family
that people could not bear to look upon,
to murder the father who engendered me.
(Ian Johnston translation)
So much for Oedipus' fate. This prophecy is mentioned several times in the play. This is what Apollo has said Oedipus will do.
As for "chance," the most common Greek word for this is tyche (also spelled tuche). Tyche is often translated as "chance," but more literally it denotes something that just happens. For example, if you were walking along and found a dollar bill, that would be considered an example of tyche. In Oedipus' case, he fled Corinth out of the fear that he might kill Polybus and he happened to be on the same road as Laius; Laius struck Oedipus, and Oedipus retaliated.
The problem is that because it was fated that Oedipus would kill his father, we may well wonder whether his ending up on the same road as Laius was fate or was it chance. Technically speaking, it seems to me that fate has to do with the prophecy and chance has to do with Oedipus and Laius happening to be in the same place at the same time. Still, I can see how a person could think that in this case "chance" and "fate" are intertwined.
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