All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Biased Coins (Posted on 2005-02-17)
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 Thoughts Steve Herman 2005-02-21 15:34:46 More part II Thoughts Steve Herman 2005-02-21 11:39:19 Part II thoughts Steve Herman 2005-02-19 10:53:43 re(3): Simple solution Steve Herman 2005-02-19 10:34:02 re(2): Simple solution Charlie 2005-02-19 02:55:00 No Subject Steve Herman 2005-02-18 23:11:25 re: Simple solution Steve Herman 2005-02-18 19:01:39 re: Simple solution Federico Kereki 2005-02-18 13:27:34 Simple solution Old Original Oskar! 2005-02-18 10:51:17
Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information