3. Eighty-eight percent of all women who submit to pregnancy tests are pregnant. A new pregnancy test

gives a false positive result with a probability of 0.02 and a correct positive result with a probability of 0.97. Define

the events: P: {a woman is pregnant} and +: {the pregnancy test is positive}.

a) Using the events and + as defined, write out the probabilities given in this problem.

b) What is the sensitivity of this test? Explain in layperson terms what this means.

c) What is the specificity of this test? Explain in layperson terms what this means.

d) What is the false negative rate (FNR) for this test? Explain in layperson terms what this means.

e) What is the unconditional probability that this test produces a positive result? Explain in layperson

terms what this means.

f) For a randomly chosen woman who receives a positive result using this test, what is the probability

that she is pregnant? Interpret this result.