Question 6 (20 points) A patient presents with symptoms of dyspnoea (shortness of breath) and is concerned about the possibility of lung cancer. The doctor acknowledges that lung cancer, tuberculosis (TB), and bronchitis are potential diagnoses for the patient's symptoms. Additionally, the doctor considers the patient's smoking history and exposure to air pollution as relevant factors. A positive X-ray result could indicate either TB or lung cancer. Assumptions: ⚫ Pollution levels are categorized as Low or High. • Variables such as Cancer, Smoking, and Dyspnoea can each be True or False. ⚫ 30% of the population seen by the doctor are smokers. X-ray results can be positive (pos) or negative (neg). ⚫ 90% of the population is exposed to low levels of pollution. • • If a patient is a smoker and exposed to high pollution levels, there's a 5% chance of having cancer. If a patient is not a smoker and exposed to high pollution levels, there's a 2% chance of having cancer. If a patient is a smoker and exposed to low pollution levels, there's a 3% chance of having cancer. If a patient is not a smoker and exposed to low pollution levels, there's a 0.1% chance of having cancer. ⚫ There's a 90% chance of a positive X-ray result if the patient has cancer. • There's a 20% chance of a positive X-ray result if the patient doesn't have cancer. • There's a 65% chance of experiencing dyspnoea if the patient has cancer. ⚫ There's a 30% chance of experiencing dyspnoea if the patient doesn't have cancer. a) Design the Bayesian Network for Lung Disease Diagnosis, following the structure outlined in Figure 13.2 on page 414 of your textbook. (10 points) b) Calculate the probability that the Cancer is detected, but pollution is low and the patient does't smoke and Xray is positive and Dyspnoea is not true. (10 points)

Fig: 1