1. You may be aware that Ray Rice (a player in the National Football League) and the National Football League (NFL) have been in the news as a result of an incident in which Rice assaulted his wife. However, you may not be aware that probability has played a role in the analysis of his court case. Rice was charged with aggravated assault, and his attorney applied for pre-trial intervention (PTI) for Rice. PTI allows the defendant to avoid conviction and jail time if they complete a set of actions (counseling, etc) prescribed by the court. Rice was granted PTI by the court, but victims rights groups are claiming that he was given preferential treatment because of his status as an NFL player (e.g., they believe that he should have been convicted of the crime and received jail time but got off easy because of his status). At issue is the following statement:

Less than 1% of domestic violence assault cases in New Jersey end with pre-trial intervention. In the past four years in New Jersey, there have been 15,029 domestic violence cases involving assault. Of those domestic violence cases involving assault, only 70, or 0.47%, have ended with the pre-trial intervention that prosecutors gave Rice. (Source: ESPN)

Let A represent the event that a court case is a domestic violence assault case.

Let T represent the event that a defendant was granted a pre-trial intervention.

Let N represent the event that a defendant is an NFL player.

How would you symbolically represent the probability reported in the italicized statement above (e.g., the 0.47%)? (3 points)

What statistical assumption are the victims rights groups making about the events T and N? (3 points)