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hw11 - CS 70 Spring 2005 Discrete Mathematics for CS...

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CS 70 Discrete Mathematics for CS Spring 2005 Clancy/Wagner HW 11 Due Thursday, April 21 Coverage: This assignment involves topics from the lecture of April 14, and from Rosen section 5.3. Administrative reminders: We will accept only unformatted text files or PDF files for homework sub- mission. Include your name, login name, section number, and partner list in your submission. Give the command submit hw11 to submit your solution to this assignment. Homework exercises: 1. (10 pts.) Quadruply-repeated ones We say that a string of bits has k quadruply-repeated ones if there are k positions where four consec- utive 1’s appear in a row. For example, the string 0100111110 has two quadruply-repeated ones. What is the expected number of quadruply-repeated ones in a random n -bit string, when n 3 and all n -bit strings are equally likely? Justify your answer. 2. (12 pts.) Stakes well done Two players, Alice and Bob, each stake 32 pistoles on a three-point, winner-take-all game of chance. The game is played in rounds; at each round, one of the two players gains a point and the other gains none. Normally the first player to reach 3 points would win the 64 pistoles. However, it starts to rain during the game, and play is suspended at a point where Alice has 2 points and Bob has 1 point. Alice and Bob have to figure out how to split the money.
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