Please help me with the questions d, e, f

wewards Online Lessons Exceptional Performance Junior Average Performance Senior Positive Junior 64 Senior Total Negative 29 103 21 84 16 280 Total 187 96 85 320 45 290 180 600 (d) (2 marks) Two students, one after another without replacement, were chosen randomly from the above sample of 600 students. What is the probability that at least one of them have exceptional academic performance or both are from junior year of study? (e) (2 marks) Two students, one after another without replacement, were chosen randomly from the above sample of 600 students. Given that at least one chosen student has excep tional academic performance, what is the probability that both chosen students are positive towards online lessons? Give your answer correct to 4 decimal places. (f) (3 marks) Another University K had reported that 45% of their students were positive towards online lessons. Carry out a simple analysis to determine whether University H had a higher proportion of students who were positive towards online lesson at the 0.05 level of significance. Assuming the null hypothesis is "The proportion of students who are positive towards online lessons at University H is 45%" , while the alternative hypothesis is "The proportion of students who are positive towards online lessons at University H is greater than 45%", carry out an appropriate hypothesis testing. Find the test statistic and determine whether the null hypothesis is rejected