4assignment - ECEN 303 Assignment 4 Problems 1 De Mrs...

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ECEN 303: Assignment 4 Problems: 1. De M´ er´ e’s puzzle. A six-sided die is rolled three times independently. Which is more likely: a sum of 11 or a sum of 12? (This question was posed by the French nobleman de M´ er´ e to his friend Pascal in the 17th century.) 2. The birthday problem. Consider n people who are attending a party. We assume that every person has an equal probability of being born on any day during the year, indpendently of everyone else, and ignore the additional compication presented by leap years (i.e., nobody is born on February 29). What is the probability that each person has a distinct birthday? 3. An urn contains m red and n white balls. (a) We draw two balls randomly and simultaneously. Describe the sample space and calcu- late the probability that the selected balls are of different color, by using two approaches: a counting approach based on the discrete uniform law, and a sequential approach based on the multiplication rule. (b) We roll a fair 3-sided die whose faces are labeled 1, 2, 3, and if k comes up, we remove k balls from the urn at random and put them aside. Descrie the sample space and
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