Just let s = 74 is ok

(a) (b) A government has 56 departments. Each department nominates 2 representatives to form a working group. 13 members are randomly selected from the working group. What is the probability that the selected 13 members are nominated by at most 12 different departments? Correct the answer to 4 decimal places. [5 marks] 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. Under 1.7 160 180 340 1.7 to 3.7 200 300I 500 Over 3.7 40 s 160 \"m- Suppose we randomly choose a student who responded to the survey. [7 marks] (i) Are the events \"1.7 S Student's GPA S 3.7\" and \"Student is from Faculty A" independent? Why? (ii) If s is the last two digits of your student number (for example, your student number is 2098765413, then 3 = 54), how to change the numbers in the above table to make the events \"Student's GPA > 3.7" and \"Student is from Faculty B\" are independent? Write down your student number. Show your new table and explain the reason. 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. [8 marks] (i) What is the probability that an individual who tests positive for virus A is infected by virus A? (ii) W'hat is the probability that an individual who tests negative for both virus A and B is healthy