Medical testing

A medical practitioner is seeing a patient that potentially has a life-threatening disease. During her medical training she was taught to recommend surgery when she is at least 70% certain the patient has the disease. The disease occurs in about 5% of the population and the best test she has at her disposal has a 99% accuracy in positively identifying patients with the disease, and a 95% accuracy in negatively identifying patients without the disease.

a)She orders one test for her patient, which turns out positive. Should she be recommending surgery for this patient? (3 points)

b)During their second meeting the patient reveals he actually has chronic asthma which somewhat complicates matters. Patients with asthma are more likely to have this disease (about 30% of them do). Further, with a pre-existing condition the test is less reliable, incorrectly identifying patients without the disease as positive 20% of the time. Does the new information change her recommendation? (1 point)

c)How confident would you be in this recommendation if you were in her place? Explain your reasoning in a short paragraph. (2 points)

d)She decides to order another test which again turns out positive. Does the recommendation stay the same? (4 points)