Question

One of the current tests for detecting COVID-19 (the RT-PCR test rather than the

antibodies test) is better than chance, but not great. The test fails to detect COVID-19 in

about 30% of patients who in fact are infected.1 But so-called "false positives" are rarer;

let's estimate that the test "detects" COVID-19 in about 0.5% of patients who are not in fact

infected. As of April 6, 2020, there were 1,266 confirmed cases of COVID-19 in B.C. by

testing.2 Since we don't know the actual prevalence of cases, let's optimistically estimate

that there are 2,500 true cases of COVID-19 in B.C. The population of B.C. is about 5 million.

Jenn (a random person in B.C.) is about to take this test. Let C be the proposition that

Jenn has COVID-19 and P be the proposition that Jenn tests positive.

(a) Using the above data, estimate Pr(C).

(b) What are Pr(P|C) and Pr(P|~C)?

(c) Using Bayes' Theorem, find the probability that Jenn has COVID-19 given that she

gets a positive test result: Pr(C|P).

Answer 1

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