1. (Check Your Intuition). An urn contains three red and three blue balls. Half the balls are removed at random and then one ball is selected from the rest. What are the chances that this ball will be red?

2. * A wooden cube with painted faces is sawed up into 1000 little cubes, all of the same size. The little cubes are then mixed up, and one is chosen at random. What is the probability of its having just two painted faces?

3. One of the numbers 2, 4, 6, 7, 8, 11, 12, and 13 is chosen at random as the numerator of a fraction, and then one of the remaining numbers is chosen at random as the denominator of the fraction. What is the probability of the fraction being in lowest terms?

4. * (Logic). Suppose six customers stand in line at a box  office, three with five-dollar bills and three with ten-dollar bills. Suppose each ticket costs 5 dollars, and the box office has no money initially. What is the probability that none of the customers have to wait for change?