Probability of disease?

Question

A test for a disease correctly diagnoses a diseased person as having the disease with probability 0.85. The test incorrectly diagnoses someone without the disease as having the disease with probability of 0.10. If 1% of the people in a population have the disease, what is the chance that a person from this population who test positive for the disease actually has the disease?

Correct response is 0.0791 but don't know how.

Answer 1

What is the probability of testing positive?
0.01 (have disease) * 0.85 (correct) + 0.99 (don't have disease) * 0.1 (wrong) = 0.1075.
What is the probability of having the disease and testing positive?
0.01 (have disease) * 0.85 (correct) = 0.0085.
So 0.0085/0.1075 = 0.0791.

Answer 2

Disease is subjective but not a subject of probabilistic study.If a diseased person is closely related to a doctor who is treating him he would expect a probability of survival close to "1" if it is highly fatal or will be contentent with anything between 0.85(85%) to 0.95(95%) which can be taken as cure for all practical purposes if a disease is chronic but not life threatening. Every body has a "body"his/her and has an ease of subjective working with "it" using it objectively for discharging personal user programmes during individual life times. When the ease is obstructed by the workings of body it is recognised by the individual and expressed subjectively which is also observed physically and diagnosed subjectively by a fellow human being of medical profession characterizing the disease by means of personal knowledge as well as data from objective pathological tests. Hence we see that the diagnosis of a disease is based on personal experience and wisdom of physician treating a patient rather than objective pathological tests and precisional accuracies of testing instruments which also multiply with probability reckonings.Mathematical formulations ,logic and solutions are all part and outcome of human mind dynamics based on rational observations and interpretations which also contain fallacies.Finally only the wisdom of human discrimination among the various phenomenal factors which decides the accuracy of diagnosis or avoid fallacy of a result in consideration of practical application.