1. Suppose that E and F are mutually exclusive events with Pr(E) = .5 and Pr(F) = .3. Find Pr(E ∪ F).
2. Of the 120 students in a class, 30 speak Chinese, 50 speak Spanish, 75 speak French, 12 speak Spanish and Chinese, 30 speak Spanish and French, and 15 speak Chinese and French. Seven students speak all three languages. A student is chosen at random. What is the probability that they speak none of these languages?
3. Of 50 fitness buffs surveyed, 15 like bicycling, 20 like jogging, and 5 like bicycling and jogging. What is the probability that a fitness buff selected at random likes only one of the two sports?