Answer to Question #152479 in Statistics and Probability for Yosef

Question

Suppose 70% of a population was vaccinated against the coronavirus, of which 4/5 (56% of all population) have been infected, and 30% did not get the vaccine, of which 1/3 (10% of all population) have been infected.

1. What is the probability that a randomly selected person has been infected?

2. What is the probability that a randomly selected person is infected given that he is vaccinated?

3. What is the probability that a randomly selected person is infected given that he is not vaccinated?

4. Is the vaccine efficient?

Answer 1

1.

P(infected) = 0.56 + 0.1 = 0.66

2.

P(infected | vaccinated) = 4/5 = 0.8

3.

P(infected | not vaccinated) = 1/3 = 0.33

4.

P(infected | vaccinated) > P(infected | not vaccinated)

Hence, vaccine is not efficient