1. * (A Waiting Time Problem). Tim, Jack, and John are going to have coffee at the local coffee shop. They will each toss a fair coin, and if one comes out as the "odd man," then he pays for all three. They keep tossing until an odd man is found. What is the probability that a decision will be reached within two rounds of tosses?

Can you generalize this with n people, a general coin with probability p of heads, and the question being what the probability is that a decision will be reached within k rounds?

2. A certain firm is looking for five qualified engineers to add to its staff. If from past experience it is known that only 20% of engineers applying for a position with this firm are judged to be qualified, what is the probability that the firm will interview exactly 40 applicants to fill the five positions? At least 40 applicants to fill the five positions?