A vaccine for a new virus is available and preliminary testing finds that among those vaccinated, only 5% become infected when exposed to the virus. Further, suppose unvaccinated individuals in your neighbourhood have a 20% chance of becoming infected when exposed to the virus. Also, suppose30% of people in your neighbourhood have been vaccinated, but you don't know for sure which ones.

1. a)Suppose you hear that someone living nearby is infected with virus, what is the chance they had already been vaccinated?
2. b)If you become infected, you will have to take off work, and this means a loss of $500 in wages. On the other hand, the vaccine is not yet free, it costs $50. Suppose you think your chance of being exposed to the virus is 75%. Is it worth getting the vaccine? Why or why not?