Happiness is defined as "something final and self-sufficient and the end of our actions," (P to D p. Happiness is not only a feeling; it is a means to an end and the result of goodness. However, where and how happiness is found, varies among the different philosophies. Can happiness be achieved by chance? No, happiness can not be reached by chance since it is only part of a proper function of man.
Goodness "is the cause of knowledge and truth," (P to D p133 lines 508e) therefore to be good is to be truthful and virtuous. When one reaches the state of Goodness one reaches happiness but, chance plays a part in this. For example, when I study as it is supposed since I am a student attending a college; I have completed part of my function and I will in return expect an excellent performance for whatever subject it is I am studying for. This completes Aristotle's philosophy that "if a function is well performed in accordance with the excellence appropriate to it: we reach the conclusion that the good of man is an activity of the soul in conformity with the excellence or virtue."(P to D p191 line1098.5) Therefore my studying has nothing to do with chance since it is only a function that I am satisfying as a student. .
Chance plays a part of my ever day life however, happiness does not come by this chance. When chance is taken there can be a change of situations and therefore if change occurs then there is no absolute truth and if there is no absolute truth then there is no good and without good happiness can not be achieved. An example of this chance is, when I believe that by taking a chance with the handsome man and forming a relationship will I be happy, since society will find him fit. According to Plato society "cannot make a man either wise or foolish: they act wholly random." (P to D p.39 line 44d) That means that society has an ever changing opinion and acts randomly therefore chance can not be taken in order to find happiness.