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. You should assume that Alice and Bob are evenly matched, so that in each round Alice and Bob each
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hw11 - CS 70 Spring 2005 Discrete Mathematics for CS...

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