For a random person from the population, what is the probability of being infected given that test result is negative?

Question

In a certain pandemic, 80% of the people are not infected and only 3% of them test positive. 95% of the infected people test positive. For a random person from the population, what is the probability of being infected given that test result is negative?

Answer 1

You are given P(~I) = .8 P(+) = .3 P(+|I) = .95 P(I|-) = ?

Bayes Law: P(I|-) = P(-|I)P(I)/P(-) = (1-.95)(1-.8)/(1-.3)