Computer Science 174 - Spring 1996 - Blum - Midterm 2

# Computer Science 174 - Spring 1996 - Blum - Midterm 2 - CS...

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CS 174, Midterm Exam #2, Spring 1996 CS 174 Spring 1996 Midterm Exam 2 Professor M. Blum Problem #1 MUFFLER MANIA (OR, TURNING 2-SIDED COINS INTO 3-SIDED COINS) Allison, Barbara, and Cindy are walking in the field one day when they find a muffler. They decide that it most likely does not belong to anyone and that one of them should keep it. They need a way to decide who should keep the muffler. Each woman should have a probability of 1/3 of keeping the muffler. They only have a fair coin as a tool. Allison proposes they toss the coin twice. If it comes up HH, Allison wins. If it comes up HT, Barbara wins. If it comes up TH, Cindy wins. If it comes up TT, it's a draw and they try again, repeatedly, until they get a winner. a) Under Allison's scheme, what is the expected number of coin tosses? Barbara has another scheme. She proposes using the coin to generate the digits of a rational number z between 0 and 1 written in base 2. For example, the coin tosses HTHTHTHHH would correspond to the number z = .101010111 .

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## This note was uploaded on 05/17/2009 for the course CS 174 taught by Professor Canny during the Spring '98 term at University of California, Berkeley.

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Computer Science 174 - Spring 1996 - Blum - Midterm 2 - CS...

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