help me...so difficult...about probability?

Question

sensitivity - the sentsitivity of a symptom is the probability that the symptom is present given that the person has a disease.

specificity - the specificity of a symptom is the probability that the symptom is not present given that the person does not have a disease.

suppose the disease is lung cancer and the symptom is cigarette smoking. if we assume 87% of people with lung cancer and 20.9% of people without lung cancer are smokers. what are the sensitivity and spesificity in this case? can cigarette smoking be used as a diagnostic tool for predicting lung cancer? why?

Answer 1

Using these numbers the sensitivity is 87% and the specificity is 79.1%.

Making judgements based on these assumptions short-circuits the search for the cause of the disease. Even using these numbers, the 13% who have lung cancer and do not smoke are far too many to dismiss, and the failure of the 20.9% to contract the disease needs to be explained.