Like usual I leave my homework until the very last minute (ahhhhh), any help is appreciated:
In 1965 the Supreme Court of the USA heard the case of Swain vs. Alabama. Swain was black and was convicted and sentenced to death for the rape of a white woman. He appealed on the grounds that there were no blacks on the jury and that no black `within the memory of persons now living has ever served on any petit jury. . . in Talladega County, Alabama'. The Supreme court rejected the appeal on the following grounds. In accordance with Alabama law the jury was selected from a panel of 100 people. There were 8 blacks on this panel. The Supreme Court ruled that the presence of 8 blacks on the panel showed that `the overall percentage disparity [between proportion of blacks on the panel and that in the population] has been small and reflects no studied attempt to include or exclude a specified number of blacks'. In Alabama at that time, only males over the age of 21 were eligible for jury service. There were about 16,000 such men in Talladega county: 26% of these were black.
(a) Calculate the probability that a random sample of 100 from this population would include 8 or fewer black men.
(b) Comment on the Supreme Court's judgement.