An outbreak of a transmissible disease has occurred in the region in which you live exposing almost the entire population. In this region 80% of people are vaccinated against the disease and 20% are unvaccinated.  Among unvaccinated people, 20% of people don't catch the disease, 60% of people have mild illness and 20% of people have a severe illness. Among people that are vaccinated 80% don't catch the disease, 10% suffer mild illness and 10% suffer serious illness.  

What proportion of people exposed to the disease will (i) suffer serious illness? (ii) suffer mild illness? (iii) avoid catching the disease? 

Assuming that mild illness costs $1000 to treat and serious illness costs $5,000 to treat. What is the expected cost per resident?  

Given that someone suffers from serious illness what is the probability that they are vaccinated?  

A radio shock jock claims that the fact that P(vaccinated | seriously ill) is greater than P(unvaccinated | seriously ill) means that the vaccine is ineffective. Explain whether this is a reasonable conclusion.