Screening test with a repeated positive result
Screening test with a repeated positive result
IP 4
10 marks
A disease affects \(2\%\) of a population. A screening test gives a positive result for \(95\%\) of people who have the disease and for \(4\%\) of people who do not have the disease.
- Find the probability that a randomly chosen person tests positive.[2]
- Given that a person tests positive, find the probability that the person has the disease. Comment on your answer.[3]
- Everyone who tests positive takes the test a second time. Assume that, for each person, the two results are independent given whether or not the person has the disease. Find the probability that a person who tests positive twice has the disease.[3]
- Explain why the assumption in (c) may not hold in practice, and state how this would affect your answer to (c).[2]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) \(0.0582\) (b) \(0.326\); most positive results are false positives (c) \(0.920\) (d) a false positive may repeat for the same person, so the results are dependent and the probability in (c) is an overestimate
Need help? Join our IP Math tuition programme.
Learn more