The sensitivity for a screening test for COVID-19 antibodies is about 0.98 and the specificity is about 0.96. It is estimated that about 25% of Manitobans have antibodies for COVID-19.

a) Suppose that a randomly selected Manitoban has a positive test result, what is the probability that this person truly has antibodies for COVID-19.

b) Suppose that a randomly selected Manitoban has a negative test result, what is the probability that this person truly has no antibodies for COVID-19.

Show all steps of the answer.

me:
Statistic’s Question:

The sensitivity for a screening test for COVID-19 antibodies is about 0.98 and the specificity is about 0.96. It is estimated that about 25% of Manitobans have antibodies for COVID-19.

a) Suppose that a randomly selected Manitoban has a positive test result, what is the probability that this person truly has antibodies for COVID-19.

b) Suppose that a randomly selected Manitoban has a negative test result, what is the probability that this person truly has no antibodies for COVID-19.

Show all steps of the answer.