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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 2SIDED COINS INTO 3SIDED 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.
 Spring '98
 Canny
 Computer Science

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