1. A city has 4050 children under the age of 10, including 514 who have not been vaccinated for measles. Sixty-five 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 th.at exactly k of the children at ABC have not been vaccina ted.
2. Country A inadvenenlly launches 10 guided missiles--6 armed with nuclear warheads--at Country B. In response, Country B fires 7 antiballistic missiles, each of which will destroy exactly one of the incomi ng rockets. The ant1ballistic missiles have no way of detecting, though, which of the 10 rockets are carrying nuclear warheads. Wha t are the chances tha t Country B will be hit by at least one nuclear missile?