Question

Enzyme immunoassay tests are used to screen blood specimens for the presence of antibodies to HIV, the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is not always correct. Here are approximate probabilities of positive and negative test results when the blood tested does and does not actually contain antibodies to HIV:

	Test +	Test -
Antibodies present	0.9951	0.0049
Antibodies absent	0.0011	0.9989

For example, the top left cell gives you the probability of getting a positive test given the antibodies are present (P(Test +|Antibodies present)).

Suppose that 1% of a large population carries antibodies to HIV in its blood.

Draw a tree diagram with this information and use it to answer the following question.

What is the probability that the test is positive for a randomly chosen person from this population? Please use 4 decimal places

Answer 1

Given that antibodies, pesentl-o-995) | 0049 Suppose thet Ix of a lavge population cnies Test t Test- bsentO ol .998 TV in us bloo 之一P(antibodies present): PCH1v) = ool and P( anh bodies absent) P(NO HV)- 0.g9 g 95) PAntibodies Prese HAnH bodses absen P = test t pc- test | "To find, pltest Positive) PCP) = o-0099SI + 0.001083 The probability that the test is positive Fandomly Chosen person hom this popul ation