During winter a particular type of virus (which we will refer to as virus V) is more likely to infect children (classied as people aged 18 or less) than adults. It is believed that, during the rst week of January, one in every 50 children without symptoms will have been infected with virus V compared to one in every 100 adults without symptoms. a) Let c be the percentage of the population who are children. Write down the formula for the percentage of the population, without symptoms, that have been infected with virus V during the first week of January. [3 marks] b) Assuming that 30% of the population are classified as children, what percentage of the population without symptoms has been infected with virus V during the first week of January? [2 marks] To minimize the spread of the virus a simple screening test is used on people who have no symptoms of virus V. For children. if the true positive rate is t% and the false positive rate is f% write down the formula for: c) The probability that a child without symptoms will test positive. [3 marks] d) The probability that a child without symptoms who has tested positive is infected with virus V. [3 marks] Now answer the following about children: e) Assuming that t=80 (i.e. the true positive rate is 80%) and #10 Ge the false positive rate is 10%) what is the probability that a child withOut symptoms will test positive for virus V? [2 marks] f) With the same assumptions as in e) what is the probability that a child without symptoms has been infected with virus V if they test positive? [2 marks] Assume that for adults the true positive rate is 90% and the false positive rate is 15%, then answer the following about adults: 9) What is the probability that an adult without symptoms will test positive? [2 marks] h) What is the probability that an adult without symptoms has virus V if they test positive? [2 marks] In the following questions assume the true and false positive rates are those stated above for children (80% and 10%) and adults (90% and 15%) respectively: i) What percentage of the population without symptoms will test positive? [3 marks] j) A child without symptoms tests negative. What is the probability they have virus V? [2 marks] k) An adult without symptoms tests negative. What is the probability they have virus V? [2 marks] I) A child without symptoms tests positive and the screening test is run a second time on the child. What is the probability they test positive in this second test? [4 marks] [Question 1 Total: 30 marks]