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 only about 5% of vaccinated children.
The following exercise is based on this information.
A group of 20 children at a nursery school are exposed to whooping cough by playing with an infected child.
Of these children 17 have been vaccinated and 3 have not.
We would like to find the probability that exactly 2 of the 20 exposed children in the previous exercise (described above) develop whooping cough.

Write down all the ways in which 2 infections can be divided between the two groups of children. Follow the pattern of the previous two questions to find the probability of each of these possibilities. Match your answers below: (V and U are the number of new infections among the vaccinated and unvaccinated children respectively.)

1. 0.1655 2. 0.0013 3. 0.5141 4. 0.7581 5. 0.1606 6. 0.4701 7. 0.3821 8. 0.8021 9. 0.0359 10. 0.2535 11. 0.5415 12. 0.4261 Enter the number of the term that corresponds to each choice:

P(V = 0 and U = 2)

P(V = 1 and U = 1)

P(V = 2 and U = 0)

Answer 1