If a randomly sampled individual from this population tests positive, what is the probability that they actually have COVID-19?

Question

Had COVID-19 but tested negative: 4

Had COVID-19 and tested positive: 166

Did not have COVID-19 but tested positive: 129

Did not have COVID-19 and tested negative: 1,218

Total adults tested in sample: 1517

Originally I thought I could multiply the chance of having COVID-19 (170/1517) by the chance of testing positive and having COVID-19 (166/1517) and ended up with 0.012

But then I was worried that I should be using Bayes' theorem and ended up with 0.14

For this type of problem, which method should I be using?

Answer 1

There are 166+129=295 who tested positive.

166 of those have covid-19.

So the conditional probability that someone in this population has covid-19, given that they tested positive, is 166/295.