At a college 72 percent of courses have final exams, 46 percent require research papers and 32 percent require both. What share require neither?

1. The union is 0.72 plus 0.46 minus 0.32, which is 0.86. 2. Courses with neither requirement form the complement of that union. 3. So the answer is 1 minus 0.86, which is 0.14 of the courses. 4. Quoting 0.86 gives the share with at least one requirement, which is the opposite of what was asked. _Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.3 Two Basic Rules of Probability_