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Due to an error in the computer program used to summon potential jurors for service, the African-American percentage (4.17%) of jury pools was only one-half their percentage (8.25%) of the age-eligible population for about fifteen months. In June 2012, in Ambrose v. Booker, the Sixth Circuit accepted the statistical evidence as sufficient to meet the requirements for a prima facie case of unfair representation the U.S. Supreme Court established in Duren. On the same day, the Michigan S. Ct. in People v. Bryant said that the statistics were insufficient. The Michigan Court accepted a new measure, the disparity of the risk (DR), of under-representation. The DR measure is shown to be extremely stringent and an alternative measure based on the probability that a jury randomly selected from the jury pool will have fewer minorities than a jury selected from the age-eligible population is proposed. The minority fraction of individuals ultimately serving on juries also depends on the fairness of the peremptory challenges made by the parties. A method for detecting unfairness is reviewed; its effectiveness depends on the number of minorities on the venire. A reanalysis of the Michigan data shows that if the proportion of African-Americans in the jury pool equaled their proportion in the age-eligible population, prosecutors could only reduce their proportion on juries to about 80% of their proportion in the population. In contrast, the criteria for adequate representativeness based on the DR measure adopted by the Michigan Court could lead to virtually no minorities serving on actual juries as only three percent of the venires would have a sufficient number of minorities to classify a prosecutor's peremptory challenging all of them as significant. Our results indicate that when assessing statistics on the demographic mix of jury pools for legal significance, courts should consider the possible reduction in minority representation that can occur in the peremptory challenge proceedings. [ABSTRACT FROM AUTHOR]