For #15, refer to this scenario. A group of 64 people were surveyed about the type of movies they prefer. 12 females preferred romantic comedies, 10 females preferred action movies, and 3 females preferred horror movies. 8 males preferred romantic comedies, 25 males preferred action movies, and 6 males preferred horror movies. 1. Construct a twoway frequency table to organize this data. 2. Suppose a person is chosen at random from this group. Let F be the event that the person is female. Find P{F]. 3. Let R be the event that the person prefers romantic comedies. Find FIR). 4. Find P{F|R} and HR] F]. Explain how these two calculations are different. 5. Are events F and R independent? Justify your answer. For #l, refer to this scenario. The middle school students in your town were surveyed and classied according to grade level and response to the question, "how do you usually get to school\"? The data is summarized in the twoway table below. 6. If a student is chosen at random from this group, what is the probability that he or she is a thgrade student who takes the bus? II". If a 6thgrade student is chosen at random from this group, what is the probability that he or she takes the bus? 3. If a student who takes the bus is chosen at random from this group, what is the probability that he or she is in l5th grade? 9. The previous three questions each have to do with 6th grade and taking the bus. Why are the answers to these questions different? 10. Are the events "being in 6th grade\" and "taking the bus\" independent? Justify your answer. J L For #1112, refer to this scenario. A new drug is coming out on the market where it proclaims to grow hair faster than anvl other alternative. In a sample of 4,000 people, 2,400 were given the drug, and of these, only 1,600 showed an'glr hair growth. The other 1,600 were given the placebo, and 1,200 of these showed hair growth. 11. Draw a twoway frequency table to illustrate the data. 12. Determine at least three conclusions you can make from the table