## Tuesday, September 28, 2004

### The Affirmative-Action Coin

In responding to my three-sided coin challenge, Patri Friedman offered another nice puzzle:
Given an unknown unfair coin, with probability p of coming up heads, where 0 < p < 1, simulate a fair coin toss. You do not know what p is, only that it is fixed.
No contest or emails this time – I’ll just post the (or an) answer in the comments section.

Glen Whitman said...

The solution: Flip two coins in sequence. If you get Heads-Tails, choose option A. If you get Tails-Heads, choose option B. If you get Heads-Heads or Tails-Tails, start over. This works because Heads-Tails and Tails-Heads both have the same probability, p(1-p), of occurring.

Anonymous said...

See there. Affimative action yields another good result. This is a great technique for us anal retentives who are always worried about an honest coin toss. Just for that reason, it always bothered me that both sides of a coin don't have the same image. Since a penny isn't worth much, I vote for making the one-cent piece two-headed. But, who's head shall it be? I'm sick of Lincoln's ugly bearded face, so I propose using Glen's head--in indian headress if he doesn't mind.(Halloween is not so far off!) I've got to contact the U.S. mint with my suggestion before they discontinue the now worthless, copper-plated penny.

Trumpit

Anonymous said...

And, if Glen won't consent to being on the penny, I'll be glad to take his place. Talk about a lopsided coin!!

Pamela Anderson

Anonymous said...

Howdy y'all. You've got to use a president's head on the penny. Clinton's head is too big. You can put mine on it but don't you dare call it unbalanced.

-GW Bush