1. From a town of 25 Republicans and 25 Democrats, pollsters A and B each sampled ten residents at random without replacement. Find the probability that the two polls contained exactly the same number of Republicans.
2. A; B; C are three events. If A is independent of B given C and if C is independent of B, are A and Bindependent events? Prove or give a counterex- ample.
3. A library patron has decided to try five libraries for a particular book. Each library has a 50% chance of having the book, and if a library has the book, there is a 20% chance that it will be checked out. Find the probability that the patron can find the book. State your assumptions.