MIT6_042JS10_lec36_prob

MIT6_042JS10_lec36_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science May 5 Prof. Albert R. Meyer revised May 4, 2010, 1304 minutes In-Class Problems Week 13, Wed. Problem 1. Let’s see what it takes to make Carnival Dice fair. Here’s the game with payoff parameter k : make three independent rolls of a fair die. If you roll a six • no times, then you lose 1 dollar. • exactly once, then you win 1 dollar. • exactly twice, then you win two dollars. • all three times, then you win k dollars. For what value of k is this game fair? Problem 2. A classroom has sixteen desks arranged as shown below. If there is a girl in front, behind, to the left, or to the right of a boy, then the two of them flirt . One student may be in multiple flirting couples; for example, a student in a corner of the class- room can flirt with up to two others, while a student in the center can flirt with as many as four others. Suppose that desks are occupied by boys and girls with equal probability and mutually
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MIT6_042JS10_lec36_prob - Massachusetts Institute of...

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