The probability that a person who is exposed to a certain contagious disease will catch it is .20.

(a) Find the probability that the 20th person exposed to this disease is the 5th one to catch it.

(b) If 20 persons are exposed to the disease, what is the expected number of persons who will catch the disease? What is the probability that exactly 5 catch it? What is the probability that more than 5 catch it?

(c) If 1000 persons are exposed to the disease, what is the probability that at least 250 catch it?

(d) What assumptions did you make in answering parts (a)-(c)?