Question

Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) indicates the patient has the condition. A negative test (–) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 201 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.

	Condition Present	Condition Absent	Row Total
Test Result +	107	23	130
Test Result –	23	48	71
Column Total	130	71	201

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Assume that the sample is representative of the entire population. For a person selected at random, find P(condition present|getting test result +). Round your answer to the nearest hundredth.

Answer 1

We have to find the probability of condition is present given that the test result is showing positive.

Let A denote the event that the condition is present.

T denote the event that the test is showing positive result.

Then we have to find P(condition present|getting test result +) i.e. P(A|T).

Now,

From the table we have,

and

Then,

Then the probability of condition is present given that the test result is showing positive is 0.823.