# Tough Probability Puzzle

1. Oct 26, 2005

### JasonJo

I know two distinct secret numbers: call them X and Y, and assume that X < Y, without loss of generality. You have no clue how I came up with them. They could be anything (positive, negative, rational, irrational, etc). They could come from any probability distribution (discrete or continuous). You have no idea. I flip a fair coin. If the coin shows Heads, I reveal to you the larger number, Y; if it shows Tails, I reveal to you the smaller number, X. You do not get to see the result of the coin flip. Your goal is to guess whether the coin was Heads or Tails, based only on your seeing the one number that I revealed to you. Obviously, if you just decide Heads'' is your guess, without taking into account the revealed number at all, then you are correct with probability 0.5. But your goal is to be able to be correct with probability {\em strictly greater} than 0.5. Devise a method to do this, and explain your solution

anyone know how to approach this? its obviously not for homework, im in an intro to prob course.

2. Oct 26, 2005

### Tide

I don't think you stand a chance unless the domain of X and Y values is finite and specified beforehand.

3. Oct 27, 2005

### JasonJo

thats what im thinking too,

i'll let you guys know what the answer is probably today if you're interested (i'm going to his office hours).

cya!

4. Oct 31, 2005

### CarlB

Never bring a knife to a gun fight.

Carl