s (b) A survey was conducted on students at two different faculties about their GPA. The following table displays data for the 1000 students who responded to the survey. GPA Faculty A Faculty B Total Under 1.7 160 180 340 1.7 to 3.7 200 300 500 Over 3.7 40 160 TOTAL 400 600 1000 Suppose we randomly choose a student who responded to the survey. (i) Are the events 1.7 3.7" and "Student is from Faculty B are independent? Show your new table and explain the reason. [7 marks] (c) There are two viruses (A and B) that can infect humans, but no one will be infected by two viruses at the same time. Anyone without these two viruses is called healthy. Doctors test a large number of people for the viruses. 90% people infected with virus A test positive for virus A and no one with virus A tests positive for virus B. 99% people infected with virus B test positive for virus B and no one with virus B tests positive for virus A. However, there are 1% healthy people test positive for virus A and 2% healthy people test positive for virus B. Assume God knows 10% humans are infected by virus A and 20% humans are infected by virus B. (i) What is the probability that an individual who tests positive for virus A is infected by virus A? (ii) What is the probability that an individual who tests negative for both virus A and B is healthy? [8 marks]