8. Suppose that and are independent events such that and . Find and . P (A B )= P (A B )= 1 0 . I t is estimated that, during the past year, % of all adults visited a therapist and % of all adults used nonprescription antidepressants. It is also estimated that % of all adults both visited a therapist and used a nonprescription antidepressant during the past year. (a) What is the probability that a randomly selected adult who visited a therapist during the past year also used nonprescription antidepressants? Round your answer to decimal places. (b) What is the probability that an adult visited a therapist during the past year, given that he or she used nonprescription antidepressants? Round your answer to decimal places. 12. Let be a random variable with the following probability distribution: Value of Find the expectation E(x) = VAR (X)= 0 0.05 1 0.05 2 0.50 3 0.10 4 0.25 5 0.05 and variance of . 13. The workers' union at a certain university is quite strong. About of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview a sample of random, to get their opinions on the strike. workers, chosen at a. Estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. 18. After the premiere of the new comedy Bumblebee, moviegoers were asked in a quick poll whether they liked the movie. Out of teenagers, adults, said they liked the movie, whereas out of said they liked the movie. __ adult or ___teenager moviegoers liked the movie less because disliked the At the movie premiere, ___% movie, whereas only of the _____adult or _____teenagers moviegoers disliked the movie ___%