There are 50 chess-club students and 60 drama-club students. If we randomly select a student, let C be the event the student is in the chess club, and let D be the event the student is in the drama club. How many students must be in both the chess club and the drama club in order for C and D to be independent events

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297