Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Beating the Odds?
Replies: 35   Last Post: Feb 6, 2013 3:44 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Paul

Posts: 387
Registered: 7/12/10
Re: Beating the Odds?
Posted: Jan 31, 2013 5:17 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wednesday, January 30, 2013 3:14:00 PM UTC, David C. Ullrich wrote:
> On Wed, 30 Jan 2013 00:29:09 -0800, William Elliot <marsh@panix.com>
>
> wrote:
>
>
>

> >There is a fair coin with a different integer on each side that you can't
>
> >see and you have no clue how these integers were selected. The coin is
>
> >flipped and you get to see what comes up. You must guess if that was the
>
> >larger of the two numbers or not. Can you do so with probability > 1/2?
>
>
>
> Of course not. Seeing one side gives you no information about
>
> what's on the other side.


I don't completely agree with this answer. The concept of a number being selected such that "you have no clue how it was selected" doesn't translate readily into mathematics. If it's mathematics, you need to specify the procedure or specify the proability space (or set of possible probability spaces) etc.

Since this isn't mathematics, the best I can do is use intuition and commonsense. Surely, if one of the numbers was > 10 ^ 1000, the most intelligent guess is that the number on the reverse side is smaller.

Here's my algorithm: If the number < 0, I will say that the number on the current face is smallest. if the number > 100, I will say that the reverse number is smallest. Otherwise, I will answer randomly.

This would probably be better than 50/50.

Alternatively (and probably a better approach), I note that there are three possible answers: A) Yes, such an algorithm exists, B) No such algorithm exists C) The problem is insufficiently specified.

You went for answer B but I would go for C.

Paul Epstein




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.