An outbreak of a transmissible disease has occurred in the region in which you live exposing almost the entire population. In this region 90% of people are vaccinated against the disease and 10% are unvaccinated.

Among unvaccinated people, 20% of people don't catch the disease, 50% of people have mild illness and 30% of people have a severe illness. Among people that are vaccinated 80% don't catch the disease, 15% suffer mild illness and 5% suffer serious illness.

1. [3 marks] What proportion of people exposed to the disease will (i) suffer serious illness? (ii) suffer mild illness? (iii) avoid catching the disease?

1. [2 marks] Assuming that mild illness costs $100 to treat and serious illness costs $10,000 to treat. What is the expected cost per resident?

1. [2 marks] Given that someone suffers from serious illness what is the probability that they are vaccinated? Show your working.

1. [3 marks] 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.