Binomial and Hypergeometric Probabilities
A city has 4050 children under the age of 10, including 514 who have not been vaccinated for measles. 65 of the city's children are enrolled in the ABC Day Care Center. Suppose the municipal health department sends a doctor and a nurse to ABC to immunize any child who has not already been vaccinated.
Find a formula for the probability that exactly k of the children at ABC have not been vaccinated.
Re: Binomial and Hypergeometric Probabilities
For this problem, you should consider that once you check one kid to see if they are vaccinated, then the probabilities of the rest will change.
This problem has a solution that deals with a topic known as sampling without replacement and for a dual choice system this is the geometric distribution (for n choices it is hypergeometric):
Hypergeometric distribution - Wikipedia, the free encyclopedia
Geometric distribution - Wikipedia, the free encyclopedia