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Biased Coins (Posted on 2005-02-17) Difficulty: 4 of 5
Call a biased coin a p-coin if it comes up heads with probability p and tails with probability 1-p. We say that a p-coin simulates a q-coin if by flipping a p-coin repeatedly (some fixed finite number of times) one can simulate the behavior of a q-coin.

For example, a fair coin can be used to simulate a 3/4-coin by using two flips and defining a pseudo-head to be any two-flip sequence with at least one real head. The chance of a pseudo-head coming up is 3/4, so we have simulated a 3/4-coin.

1. Find a rational value p such that a p-coin can simulate both a 1/2-coin and a 1/3-coin, or prove that no such value exists.

2. Find an irrational value p such that a p-coin can simulate both a 1/2-coin and a 1/3-coin, or prove that no such value exists.

See The Solution Submitted by David Shin    
Rating: 4.0000 (3 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Final Part II ThoughtsSteve Herman2005-02-21 15:34:46
More part II ThoughtsSteve Herman2005-02-21 11:39:19
Part II thoughtsSteve Herman2005-02-19 10:53:43
re(3): Simple solutionSteve Herman2005-02-19 10:34:02
re(2): Simple solutionCharlie2005-02-19 02:55:00
SolutionNo SubjectSteve Herman2005-02-18 23:11:25
Some Thoughtsre: Simple solutionSteve Herman2005-02-18 19:01:39
Some Thoughtsre: Simple solutionFederico Kereki2005-02-18 13:27:34
SolutionSimple solutionOld Original Oskar!2005-02-18 10:51:17
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