1. (10 points) Of a population of consumers, 20% are known to prefer a particular brand A of toothpaste. A series of interviews is conducted on randomly selected customers. Assume each person's preference is independent of any other person. (a) Find the probability that exactly six people have to be interviewed to en- counter the first consumer who prefers brand A. (b) On average, how many people do we expect to interview to encounter the first consumer who prefers brand A?