8. One-half percent of the population has AIDS. There is a test to detect AIDS. A positive test result is supposed to mean that you have AIDS but the test is not perfect. For people with AIDS, the test misses the diagnosis \( 2 \% \) of the times. And for the people without AIDS, the test incorrectly tells \( 3 \% \) of them that they have AIDS. (9 marks) (a) What is the probability that a person picked at random will test positive? (4 marks) (b) What is the probability that you have AIDS given that your test comes back positive? (4 marks)
Added by Dancan N.
Close
Step 1
- One-half percent (0.5%) of the population has AIDS. - The test misses the diagnosis of AIDS 2% of the time for people who actually have AIDS. - The test incorrectly indicates AIDS in 3% of the people who do not have AIDS. Show more…
Show all steps
Your feedback will help us improve your experience
Christopher Stanley and 96 other Probability educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Recommended Videos
Suppose that 8$\%$ of the patients tested in a clinic are infected with HIV. Furthermore, suppose that when a blood test for HIV is given, 98$\%$ of the patients infected with HIV test positive and that 3$\%$ of the patients not infected with HIV test positive. What is the probability that a) a patient testing positive for HIV with this test is infected with it? b) a patient testing positive for HIV with this test is not infected with it? c) a patient testing negative for HIV with this test is infected with it? d) a patient testing negative for HIV with this test is not infected with it?
Discrete Probability
Bayes’ Theorem
In a large city, $8 \%$ of the inhabitants have contracted a particular disease. A test for this disease is positive in $80 \%$ of people who have the disease and is negative in $80 \%$ of people who do not have the disease. What is the probability that a person for whom the test result is positive has the disease?
It is believed that $3 \%$ of a clinic's patients have cancer. A particular blood test yields a positive result for $98 \%$ of patients with cancer, but it also shows positive for $4 \%$ of patients who do not have cancer. One patient is chosen at random from the clinic's patient list and is tested. What is the probability that if the test result is positive, the person actually has cancer?
Probability
Are Mutual Exclusiveness and Independence Related?
Recommended Textbooks
Probability with Applications in Engineering, Science, and Technology
Probability and Statistics for Engineers and Scientists
Applied Statistics and Probability for Engineers
Watch the video solution with this free unlock.
EMAIL
PASSWORD