Question

2. A ventilation perfusion scan is used to generate the probability of pulmonary embolism (PE) in patients. Based on the result of the scan, patients are classified as high prob- ability for PE, moderate probability for PE, and low probability for PE. Consider the following data, classified by patient's age: Age Scan 45-54 55-64 65-74 High Prob. for PE 13 15 20 Moderate Prob. for PE 14 18 Low Prob. for PE 25 20 31 Is a patient is selected at random, find the probability that a. The patient has a high probability for PE. [1] b. Th patient is at least 55 years of age. [1] c. The patient has a high probability of PE given that the patient is at least 55 years of age. [1] d. Are the events high probability for PE and at least 55 years of age independent? Justify your answer. [1]