1. Twelve vegetable cans, all of the same size, have lost their labels. It is known that five contain tomatoes and the rest contain beets. What is the proba- bility that in a random sample of four cans all contain beets?
2. * (Domination of the Minority). In a small town in Alaska, there are 60 Republicans and 40 Democrats. Ten are selected at random for a council. What is the probability that there will be more Democrats on the council than Re- publicans?
3. (Negative Hypergeometric Distribution). In a small town in Alaska, there are 60 Republicans and 40 Democrats. The mayor wants to form a council, selecting residents at random until five Democrats have been chosen. Find the distribution and the expected value of the number of Republicans in the council and hence the distribution and the expected value of the size of the council.