Question

Testing for HIV: Enzyme immunoassay (EIA) 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 not always correct. Here are approximate probabilities of positive and negative EIA outcomes when the blood tested does and does not actually contain antibodies to HIV:

test result
+ -
antibodies present 0.9985 0.0015
antibodies absent 0.0060 0.9940

Suppose that 1% of a large population carries antibodies to HIV in their blood. Draw a tree diagram for selecting person from the population and testing his or her blood.

Answer 1

Tree diagram helps visualize the probabilities associated with HIV antibody testing and the potential for misdiagnosis due to test limitations.

Tree Diagram for HIV Testing

Here's the tree diagram for selecting a person from the population and testing their blood for HIV antibodies, considering the given probabilities:

Select Person (1.0)

|

----------

/ \

Antibodies Present (0.01) Antibodies Absent (0.99)

| |

---------- ----------

/ \ / \

Test Positive (0.009985) Test Negative (0.000015) Test Positive (0.00594) Test Negative (0.98406)

Step-by-step explanation:

The starting node represents selecting a person from the population with probability 1.0.

The person either has antibodies present (probability 0.01) or doesn't (probability 0.99).

For those with antibodies, there's a chance of a positive test (0.009985) or a negative test (0.000015).

Similarly, for those without antibodies, there's a chance of a positive test (0.00594) or a negative test (0.98406).

This tree diagram visually represents the probabilities of different test outcomes based on the presence or absence of HIV antibodies in the selected person.

It highlights that even with a highly accurate test, there's still a small chance of false positives and negatives.

Additional Notes:

This is a simplified model and doesn't account for all factors that can influence HIV testing, such as different test generations or individual variations.

The prevalence of HIV antibodies in the population may vary depending on the specific context.

It's important to interpret HIV test results in conjunction with other clinical information and risk factors.