1. Sam tosses two fair dice and Fred tosses one. Sam wins if his sum is at least twice as much as Fred's score. What is the probability that Sam wins?
2. A statistics department has five assistant professors, two associate professors, and six full professors. Two of these 13 faculty members are chosen at random. What is the probability that the junior member is an assistant professor if the senior member is a full professor? It is assumed that we know that the two chosen are always of different ranks.
3. * (Lottery). In a state lottery, five numbers from 00; 01; : : : ; 49 are selected at random. Someone holding exactly those five numbers wins. For how many weeks must a couple buy tickets to have a 5% probability that at least one of them wins at least once?