Question

Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cause of childhood deaths before the development of vaccines. About 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to about 5% of vaccinated children. A group of 20 children at a nursery school are exposed to whooping cough by playing with an infected child (assume the infected child is NOT one of these 20). Of these children, 15 have been vaccinated and 5 have not.

1. What is the probability that exactly 5 of the vaccinated children are infected with whooping cough from this exposure?
2. What is the mean number of new infections among the 15 vaccinated children? Among the 5 unvaccinated children?
3. What is the expected number of new infections from this group of nursery school after being exposed to the infected child?

Answer 1