What are incidents that occur from chance and that occur from choices made by the characters in Shakespeare's Romeo and Juliet?
In pretty much every occurrence in the play, Shakespeare overlaps both choice and chance. In other words, perhaps a few things happen by chance, but the choices of the characters either lead to the chance occurrences, or they make the consequences of the chance occurrences much worse.
The love affairs in the play are good examples of chance occurrences. Romeo falls in love with, and is rejected by, Rosaline purely by chance. Some will argue that we cannot choose whom we fall in love with, therefore, falling in love is purely a matter of chance. However, we certainly do have control over how we handle our emotions of both love and grief. Romeo made the choice to allow Rosaline's rejection to drive him into such mad grief and dispair that he pined for her night after night. Romeo's father said that Romeo was seen again and again crying at dawn under a tree in a certain part of town (I.i.127-129). Hence, while Romeo falls in love with Rosaline by chance, he make the choice to react so strongly.
Similarly, Romeo falls in love with Juliet by chance. However, both he and his friends made the choice, against Romeo's better judgement, to crash the Capulet's ball. Romeo proves that he felt it was a bad idea to crash the ball when he very prophetically states,
I fear, too early; for my mind misgives
Some consequence, yet hanging in the stars,
Shall bitterly begin his fearful date... (I.iv.115)
Romeo was correct in hesitating to crash the ball, for that one decision leads to many deaths. Hence, while falling in love with Juliet was a matter of chance, crashing the ball, which led to both meeting Juliet and many deaths was a matter of choice that could have been avoided.
We also see chance and choice intertwined in Juliet's faked death. For Juliet, it was a matter of chance that a marriage to Paris was being forced on her by her father, immediately after having secretly married Romeo. However, it was her father who made the choice, against his own initial better judgement, to make her marry at the age of 12. Juliet's father first tells Paris to "[l]et two more summers" pass before "we may think her ripe to be a bride" (I.ii.10-11). Hence, her father's choice leads Juliet to seek drastic measures.
Also, Friar Laurence makes the choice to suggest faking her death to get her out of her predicament, rather than confiding in her father about the marriage. While it was a matter of chance that the plot went awry, the plan itself was a matter of choice. Friar Laurence also made the choice to deliver the vital news of Juliet's faked death to Romeo via a messenger. While it was a matter of chance that his fellow friar was detained from getting to Mantua in time, it was Friar Laurence's choice that ultimately led to Romeo not receiving the information.