Question

A survey shows that 80% of a population has been vaccinated against the flu, but 5% of the vaccinated population gets the flu anyway. In total 10% of the population gets the flu. Let V be the event that a randomly selected person in the population has been vaccinated and F the event that a randomly selected person in the population gets the flu.

(a) Present the information using either a Venn diagram or a table or both.
(b) Estimate the following probabilities and describe the probabilities in words.

• P(F 0 )
• P(F ∩ V )
• P(F ∩ V 0 )
• P(F|V )
• P(V |F)

(c) Does this survey provide evidence that the events F and V are not independent? Give a reason for your answer.
(d) Which conditional probabilities will you calculate to explain whether vaccination should be encouraged

Answer 1