Question 5 Assume that among all 60-year old man with lung cancer, 90% have symptoms of a chronic cough and occasional breathlessness. Suppose that among all 60-year old man with sarcoidosis, 90% have symptoms of a chronic cough and occasional breathlessness. Among all 60-year old man without the two diseases, 0.1% have symptoms of a chronic cough and occasional breathlessness. Besides, 0.1% of 60-year-old, never-smoking men have lung cancer, and 0.9% of 60-year-old, never-smoking men have sarcoidosis. More- over, assume that having lung cancer and having sarcoidosis are mutually exclusive. Suppose a 60-year-old man who has never smoked cigarettes presents to a physician with symptoms of a chronic cough and occasional breathlessness. The physician becomes concerned and orders the patient admitted to the hospital for a lung biopsy. What is the probability that the man does not have the two diseases? (A). 1.00%; (B). 99.00%; (C). 81.08%; (D). 9.91%; (E). 9.01%