A county is 50% African-American and 50% Caucasian, and an African-American is on trial. A jury has been selected that contains six Caucasians and two African-Americans (this is an 8 person jury). The defendant claims racial bias in the jury selection because its makeup seems unlikely given the racial percentages in the county. However, the prosecutor claims that the jury was selected without regard to race. Is the defendant's claim credible? In other words, is selecting 2 or fewer African-Americans unlikely to happen by chance? The defendant needs to know these probabilities in order to see if he should pursue his claim.

Method 1: Calculate a theoretical probability by using the binomial formula

Method 2: Perform a simulation and compare results with the "true" probabilities computed in Method 1.

You will compare these probabilities to each other, make a decision, and advise the man.

Should the defendant pursue his claim of racial bias in jury selection or should he stick with the jury that was selected because most likely it just happened by chance? Make sure that you provide a solidstatistical support for you decision, please include in your report results for the actual probabilities and the probabilities obtained from the simulation.