Researchers at the University of South Florida Center for Biological Defense have developed a safe method for rapidly detecting anthrax spores in powders and on surfaces (USF Magazine, Summer 2002). The method has been found to work well even when there are very few anthrax spores in a powder specimen. Consider a powder specimen that has exactly 10 anthrax spores. Suppose that the number of anthrax spores in the sample detected by the new method follows an approximate uniform distribution between 0 and 10.
a. Find the probability that 8 or fewer anthrax spores are detected in the powder specimen.
b. Find the probability that between 2 and 5 anthrax spores are detected in the powder specimen.