# screening test for a disease example

Consider a screening test for a disease. The sensitivity of the test is 80%. The specificity of the test is 95%. The disease is present in 0.1% of the population. Use the following events for a patient receiving the screening test;

D they have the disease DC they do not have the disease P their test gives a positive result C their test gives a negative result

(a) Write the three statements given in the introduction of the question as probability or conditional probability statements (whichever is appropriate), using the events above.

(b) What is the probability a patient has the disease and their test gives a positive result? Show working.

(c) What is the probability a patient does not have the disease and their test gives a positive result? Show working.

(d) What is the probability that a patient receives a positive result? Show working.

(e) If a patient receives a positive result, what is the probability that they have the disease? Show working.

(f) What does this suggest about the screening test?