In the beginning of May 2020, the Public Health Agency in Sweden (Folkhälsomyndigheten) estimated that 1% of the population had been infected by the corona virus, and decided to create an antibody...

Extracted text: In the beginning of May 2020, the Public Health Agency in Sweden (Folkhälsomyndigheten) estimated that 1% of the population had been infected by the corona virus, and decided to create an antibody test. Research showed that if a person has antibodies, the test will give a positive result (i.e. indicate that the person has antibodies) with probability 99 %. Also, if a person does not have antibodies, the test will give a negative result (i.e. indicate that the person does not have antibodies) with probability 98 %. a) What proportion of all tests will give a positive result? b) If a person gets a positive test result, what is the probability that the person has antibodies?