1. A local lottery is conducted weekly by choosing five chips at random and wit hout replacement from a population of 40 chips, numbered 1 through 40; order does not matter. The winning n umbers are announced on five successive commercials d uring the Monday nigh t broadcast of a televised movie. Suppose the first three winning numbers match three of yours. What are your chances at that point of win ning the lottery?
2. A display case contains 35 gems, of which lO are real diamonds and 25 are fake diamonds. A burglar removes four gems at random, one at a time and without replacement. Wha t is the probability thal the last gem she steals is the second real diamond in the set of four?