Question 2. [12 marks] Rheumatoid arthritis is a long-term autoimmune disorder that typically results in Warm, swollen, and painful joints. A GALS examination assesses the gait, arms, legs and spine of patients in an attempt to diagnose rheumatoid arthritis. Research into the eeetiveness of the GALS procedure to detect rheumatoid arthritis when used by physiotherapists and physiotherapy students was conducted in 2011. If interested, the article can be found here: https : //doi . org/10. 1016/] .physio . 2010. 11 . 008. From the article, one might estimate that the sensitivity and specicity of the procedure are 77% and 80% respectively. The article also indicates that the prevalence of rheumatoid arthritis is estimated at around 1%, that is if we randomly select someone from the population, the probability they have rheumatoid arthritis will be 1%. Use the following notation to represent the events for this scenario: D - they have the disorder; DC - they do not have the disorder; P - the GALS procedure gives a positive result; and, PC - the GALS procedure gives a negative result. (a) [3 marks] In the introduction of the question there are three probability statements about: sensitivity: specicity; and prevalence. Write these statements using mathematical notation and the denition of the events above (b) [3 marks] Construct a tree diagram for the above scenario. Clearly label the arms representing sensitivity and specicity. (e) [3 marks] A randomly selected individual is assessed using the GALS procedure and this results in a positive diagnosis, that is the patient is believed to have rheumatoid arthritis. Given the positive result, what is the probability that patient actually has rheumatoid arthritis? (d) [3 marks] Rather than someone who is randomly selected, an individual presents at a physio- therapy practice with aches and pains in their joints, a symptom of rheumatoid arthritis. The GALS examination process is applied to the patient and results in a positive outcome. If you were to calculate the probability the patient has rheumatoid arthritis given the positive result, would the probability be more or less than the value you calculated in part (c)? Explain your reasons for this. (-0\" I77. .53 - 0.006% % ('Usv'hI-13- o'WSQ ('01-131'0' o'\"\\\" % (Mi'nl'n - 04M\" (-uu-vu-nsO-W ("I'h-'l'l'l\" 0'51 (0\" ,43'4) : 0J7). Mn ms: -2) 9 095 - Random individual is assessed using the GALS procedure - Assessment results in positive diagnosis (believed to have arthritis) - What is the probability that the patient actually has rheumatoid arthritis? - Mathematical notation? d) - Individual has symptoms of arthritis - Has a positive results of having arthritis - Mathematical notation