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HW02_2011 - PROF Y HONG FALL 2011 ECONOMICS 6190 PROBLEM...

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PROF Y. HONG FALL 2011 ECONOMICS 6190 PROBLEM SET # 2 1. A secretary types four letters to four people and addresses the four envelopes. If he inserts the letters at random, one into each envelope, what is the probability that exactly two letters will go into the correct envelopes? Exactly three? 2. An elevator in a building starts with °ve passengers and stops at seven ±oors. If each passenger is equally likely to get o/ at any ±oor and all passengers leave independently of each other, what is the probability that no two passengers will get o/ at the same ±oor? 3. Suppose that a box contains r red balls and w white balls. Suppose also that balls are drawn from the box one at a time at random, without replacement. (1) What is the probability that all r red balls will be obtained before any white balls are obtained? (2) What is the probability that all r red balls will be obtained before two white balls are obtained?
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