A test for a relatively rare disease involves taking from the patient an appropriate tissue sample which is then assessed for abnormality. A few sources of error are associated with this test. First, there is a small, but non-zero probability, θs, that the tissue sampling procedure will miss abnormal cells primarily because these cells (at least in the earlier stages) being relatively few in number, are randomly dis- tributed in the tissue and tend not to cluster. In addition, during the examination of the tissue sample itself, there is a probability, θf , of failing to identify an abnor- mality when present; and a probability, θm , of misclassifying a perfectly normal cell as abnormal.
If the proportion of the population with this disease who are subjected to this test is θD ,
(i) In terms of the given parameters, determine the probability that the test result is correct. (Hint: ?rst compute the probability that the test result is incorrect, keeping in mind that the test may identify an abnormal cell incorrectly as normal, or a normal cell as abnormal.)
(ii) Determine the probability of a false positive (i.e., returning an abnormality result when none exists).
(iii) Determine the probability of a false negative (i.e., failing to identify an abnor- mality that is present).