Note: In answering these questions, give more than just a numerical answer. If you use symbols to stand for certain phrases, for example P(C) = Probability that a patient has cancer be sure the meaning is clear. Show the thought processes you are using by brief reference to the appropriate rule or definition or by stating the problem in terms of "AND" and "OR", etc. 1. A random sample of people were measured for significant lung blockage and the people were divided into two categories, smoking and non-smoking. The following results were observed. Non-Smoking Smoking Normal Lungs 95 48 Lung Blockage Observed 45 230 Let S be the event that a person smokes. Let LB be the event that the person has significant lung blockage observed. a) Determine P(NOT LB) b) Determine P(S) c) Determine P(LB AND S) d) Determine P(NOT LB OR NOT S) e) Determine P(NOT LB AND LB) f) Determine P(S | NOTLB) g) Determine P(LB | S) h) Are events LB and S independent events? Why or why not? Determine mathematically not just what you think. i) Give one example of two mutually exclusive events from the above table and explain why they are mutually exclusive. 2. The specificity and sensitivity of thallium-201 myocardial perfusion imaging (MPI), under exercise, in patients with suspected coronary-obstructive disease has a specificity 97% and sensitivity 79%. If the prevalence of coronary-obstructive disease is 12% in patients seen in emergency. a. What is the probability that the patient is suffering coronary-obstructive disease given the MPI test result is positive? b. What is the probability that the patient is suffering coronary-obstructive disease you know the MPI test result was negative? C. What is the probability of a false positive result using this test? d. Create a 2x2 table similar to Table 4-2 in the text assuming you have a total of 1000 subjects