4. + is] A fair octagonal (eight sided) die, with faces marked 1 to 8, is thrown as an experiment, the result being the number on the face on which the die rests. The following events are defined: E, = (1, 2, 3, 4, 5}; E, = (2, 4, 6, 8); E, = (1, 3, 5, 7). Find the following: A. [2] P(E, E,) B. [2] P(E, E; ) C. [2] P( E, | E, ) D. [2] P(E, E,) E. [2] P(E, |(E,orE2 )) F. [2] P(E,| E,) 5. [-Marks] Trends In International Mathematics and Science Study (TIMSS) is a study that involves more than 60 countries. The purpose of the study is to assess the performance of Grade 4 and/or Grade 8 students in mathematics and science and report on both subjects separately. In TIMSS2019, average mathematics score obtained from the sample of Grade 4 Canadian students was 512 with standard error 1.9. The average score obtained from the sample of Grade 4 Italian students was 515 and standard error 2.4. Note that both sample sizes are higher than 30. A. [ Obtain a 90% confidence interval for the difference between the average scores for Grade 4 Canadian and Italian students. B. At a = 0.05, is there evidence that on average Grade 4 Italian students score higher than Grade 4 Canadian students? 6. (1aks] In a clinical trial to test headaches as a side effect of a new drug to treat allergies, 2280 patients were randomly divided into 2 equally sized groups. Group 1 received the medication and received a placebo. Of the 1140 patients in Group 1, 24% indicated having headaches, while 16% of Group 2 reported having headaches. A. PI Is there enough evidence to conclude that the proportion of patients who take the medication and get headaches is higher than those who don't take the medication? Use a = 0.01 B. [ Compute the 95% confidence interval for the difference in proportions of patients who get headaches with or without the drug