Question

A corona virus antibody test is such that it detects the antibody, i.e. with a positive...

A corona virus antibody test is such that it detects the antibody, i.e. with a positive result, in 100% of the individuals who actually have the antibody.

Also, if a person does not have the antibody, the test will report that he or she does not have it, i.e. with a negative result, with probability 0.996.

Suppose that 7.3% of the population has indeed the antibody.

If a person is chosen at random from the population and the antibody test indicates that she has the antibody, i.e. with a positive result, what is the conditional probability that she does, in fact, have the antibody?

A full, well-motivated solution is required

Math   Statistics-And-Probability   
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Answer #1

To calculate the required probability we will use Bayes theorem on conditional probability.

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