Scientific research on popular beverages consisted of 70 studies that were fully sponsored by the food industry, and 30 studies that were conducted with no corporate ties. Of those that were fully sponsored by the food industry, 10 % of the participants found the products unfavorable, 21 % were neutral, and 69 % found the products favorable. Of those that had no industry funding, 39 % found the products unfavorable, 17 % were neutral, and 44 % found the products favorable. What is the probability that a participant selected at random found the products favorable? If a randomly selected participant found the product favorable, what is the probability that the study was sponsored by the food industry? If a randomly selected participant found the product unfavorable, what is the probability that the study had no industry funding?

(2 points) On average 68 % of Finite Mathematics students spend some time in the Mathematics Department's resource room. Half of these students spend more than 90 minutes per week in the resource room. At the end of the semester the students in the class were asked how many minutes per week they spent in the resource room and whether they passed or failed. The passing rates are summarized in the following table: Time spent in resource room Pass % None Between 1 and 90 minutes More than 90 minutes If a randomly chosen student did not pass the course, what is the probability that he or she did not study in the resource room? Answer: C] (3 points) In a survey of 283 people, the following data were obtained relating gender to political orientation: Republican (R) Democrat (D) Independent (I) Total Male (M) 69 Femal (F) 78 Total 1 47 A person is randomly selected. What is the probability that the person is: a) Male? C] b) Male and a Democrat? C] 0) Male given that the person is a Democrat? d) Republican given that the person is Male? e) Female given that the person is an Independent? 1') Are the events Male and Republican independent? Enter yes or no