Question

The International Committee on the Taxonomy of Viruses estimates that 8.3% of the US population has COVID 19. The Center for Disease Control and Prevention has developed a diagnostic test for COVID 19 that is 98% accurate for people who have COVID 19 and 95% accurate for people who don't have it. The Center gives the test to a randomly selected person. What is the probability that diagnosis is correct? Round your answer to hundredth percent.

Answer 1

Let's first define some events:

A: The person has COVID-19.

B: The test result is positive.

Using the information provided, we can calculate the probability of a correct diagnosis using Bayes' theorem:

P(A|B) = P(B|A) * P(A) / [P(B|A) * P(A) + P(B|not A) * P(not A)]

where P(B|A) is the probability of a positive test result given that the person has COVID-19, P(A) is the prevalence of COVID-19 in the population (0.083 or 8.3%), P(B|not A) is the probability of a positive test result given that the person does not have COVID-19 (false positive rate, 0.05 or 5%), and P(not A) is the complement of P(A) (0.917 or 91.7%).

Plugging in the values, we get:

P(A|B) = (0.98 * 0.083) / [(0.98 * 0.083) + (0.05 * 0.917)]

= 0.6037 or 60.37%

Therefore, the probability that the diagnosis is correct is 60.37%, rounded to the nearest hundredth percent.