1. Kate normally smokes one cigarette per hour, but she wants to cut down. Her friend
John suggests that she try the following scheme:
Each hour, roll a fair die. If a 1 or a 2 comes up, do not smoke a cigarette
that hour. Otherwise, smoke a cigarette as you normally would.
Kate has a pack of 20 cigarettes. What is the probability that the pack lasts at least
24 hours? What are the mean and the variance of the number of hours that the pack
lasts?
2. John wins 1/3 of the points when he plays table tennis against Kate and the first
player to reach 21 points wins the game (note that we do not require the winner to
have at least a two point advantage). Supposing that the outcomes of the points
played are independent, what is the probability that John will win his next game
against Kate?
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