Question: 1. A warehouse has a stock of n items of a certain kind, r of which are defective. Two of the items are chosen at random, without replacement. What is the probability that at least one is defective? Show that for large n the number is very close to that for selection with replacement, which corresponds to two Bernoulli trials with pobability p = r/n of success on any trial.
2. A coin is flipped repeatedly, until a head appears. Show that with probability one the game will terminate.
Tip: The probability of not terminating in n trials is qn.