Question

One of your tree planting buddies has suggested that every person in Canada should be tested for COVID-19 so we get a true, accurate, picture of who has the disease. I don't know the actual numbers but (in order to be as generous as possible) let's assume that the test is extremely accurate so that if you have COVID-19 it will show a positive result 99% of the time and if you don't have COVID-19 it will be positive only 2% of the time. Let's also assume that the prevalence of COVID-19 in the Canadian population at the time of testing is 1 in 1,000. If we had enough test kits to do such testing on the whole population of Canada, explain to your buddy how likely a person would be to have COVID-19 if he or she showed a positive test result.

Answer 1

Probability that a randomly selected person in Canada has Covid= 1/1000 = 0.001

So, the probability that the person does not have Covid= 1-0.001= 0.999

Now, If the person has Covid, the test kit gives positive result with Probability 0.99

If the Person does not has Covid, the test shows positive results with Probability 0.02

So using Bayes Theorem, we want

, P(Has Covid|Positive Result) =

P(Has Covid and Positive Result)/P(Positive Result)

Where P(Positive) = P(has Covid and positive) + P(does not have Covid and positive)

So required Probability is,

= 0.001*0.99/(0.001*0.99 + 0.999*0.02)

= 0.0472