. The table summarizes the relationship between two categorical variables, grade level and the student's answer to the question, "Do you cat regularly in the school cafeteria?" Grade 10 11* 12 Total Fat in 130 175 127 405 cafeteria? NO 34 88 170 310 Total 1 48 209 210 238 305 (a) If you choose a student at random, what is the probability he or she eats regularly in the cafeteria? (b) If you choose a student at random, what is the probability the or she eats regularly in the cafeteria, given that he or she is in 10- grade? (e) If you choose a student at random, are the events " 10" grade" and "cats regularly in the cafeteria" independent? Explain how you know. 12. Mrs. Chavis's statistics class han 26 students in it, 14 girls and 12 bays. She uses a calculator to select two students it random to solve a problem on the board (a) What is the probability that both students are girls? (b) Given that the second student chosen is a girl, what is the probability that the first student was also a girl? Starnes Taber, Updairal Version of The Proctier of Statistics, bike G 3030 AFW Publishers Inc. 13. On Mr. Casper's debate team at Thunderbird High School, 20%% of the members are sophomores, 35%% are juniors and 45%% are seniors. A team member is selected randomly to give the closing argument for the team. Ifa sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. Ifa junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.35. (a) Find the probability that the team wins the debate