Question

A covid-19 vaccination reduces the probability of getting covid-19 infection from 0.4 to 0.1. In a city, 45% people are vaccinated. Then the probability that a non-vaccinated person chosen at random in the city gets covid-19 infection is

• A. 0.55
• B. 0.24
• C. 0.32
• D. 0.4
• E. 0.18

Answer 1

The Correct Option is D

We are given the following information: 

• The probability of getting a COVID-19 infection for a vaccinated person is reduced from 0.4 to 0.1.
• 45% of people in the city are vaccinated.
• We need to find the probability that a non-vaccinated person, chosen at random, gets a COVID-19 infection.

Let:

• \(P(\text{Infection | Vaccinated}) = 0.1\)
• \(P(\text{Infection | Non-Vaccinated}) = 0.4\)
• The probability that a person is vaccinated is 45%, or \(P(\text{Vaccinated}) = 0.45\).
• The probability that a person is non-vaccinated is 55%, or \(P(\text{Non-Vaccinated}) = 0.55\).

We are asked to find the probability that a non-vaccinated person gets COVID-19. Since we are only concerned with non-vaccinated people, the answer is simply the probability of infection for non-vaccinated people:

\(P(\text{Infection | Non-Vaccinated}) = 0.4\)

The probability that a non-vaccinated person chosen at random in the city gets COVID-19 infection is 0.4.