(Solved): (b) The table below shows some of the relative frequencies of student respons ...

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(b) The table below shows some of the relative frequencies of student responses to the teacher's survey. (1 Point) i) What is the probability that a randomly selected student did at least 30 minutes of homework at night given that the student's course grade was a B? ( 1 point) ii) Are the events "did at least 30 minutes of homework" and "course grade is a B" independent? Explain your answer. c) Based on the results from parts (a) and (b), what should the teacher conclude about the association between a student's course grade and whether or not the student did at least 30 minutes of homework? d) The school's principal is conducting some focus groups and will randomly choose 3 students from math classes. Assume that the 3 students will be chosen from the group of students who answered the survey above. i) What is the probability that all 3 students selected had a course grade of an A and did at least 30 minutes of homework each night? $$(1$$ point) ii) Suppose that you know these probabilities: (2 points) - The probability that 1 student out of the 3 had a course grade of an A and did at least 30 minutes of homework each night is $$0.4239$$. - The probability that 2 students out of the 3 had a course grade of an A and did at least 30 minutes of homework each night is $$0.3069$$. What is the probability that none of the 3 students selected had a course grade of an A and did at least 30 minutes of homework each night? Explain the work leading to your answer.