Suppose in a community of 2000 adults, 1400 are fully vaccinated against COVID-19, 400 are partially

vaccinated, and 200 are unvaccinated. Suppose there are 42 adults in the community who are in the

hospital because of COVID-19, of whom 14 are fully vaccinated, 8 are partially vaccinated, and 20

are unvaccinated.

Let H be the event that an adult in this area requires hospitalisation for COVID-19. Let V be the

event that an adult in this area is fully vaccinated, D be the event than an adult in this area is

partially vaccinated, and U be the event that an adult in this area is unvaccinated.

(a) Construct a contingency table that summarises the given information.

(b)Show that the probability that a randomly selected fully vaccinated adult is in the

hospital because of COVID-19 is 0.01.

(c)Show that the probability that a randomly selected partially vaccinated adult is in

the hospital because of COVID-19 is 0.02.

(d)Show that the probability that a randomly selected unvaccinated adult is in the

hospital because of COVID-19 is 0.1.

(e) Find the probability that a randomly selected adult is unvaccinated and in the

hospital because of COVID-19.

(f)Find the probability that a randomly selected adult hospitalised because of COVID19 is unvaccinated.

(g) Someone reading a report of this data set notes that a majority of the people in the

community hospitalised for COVID-19 have had at least one vacciation and argues that this is

evidence that the vaccines do not work effectively. Using the given information and your answers

to the previous questions, argue why this is not an appropriate interpreation.