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

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,634 Registered: 1/8/12
Re: Beating the Odds?
Posted: Jan 31, 2013 3:23 AM

On Wed, 30 Jan 2013, forbisgaryg@gmail.com wrote:
> On Wednesday, January 30, 2013 12:29:09 AM UTC-8, William Elliot 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?

>
> Well, there was the monty hall problem years ago. Suppose there are 3
> keys and you have to choose one. One of the three turns on a car's engine
> where the other two do not. After you choose a key Monte takes one and
> tries it in the car and it doesn't turn over the engine. He then asks
> you if you'd like to change your mind. What should you do? You should
> change your mind because the first key you chose had a one in three chance
> of turning on the car where the remaining key has a two in three chance.
>
> Soo...
>
> Assuming the coin only has positive integers then you should guess
> the number showing is the smaller integer because there are more
> integers greater than x than there are less than x and this is true
> for all positive integers x.
>

Recall, you have no clue how the integers were selected much less that
both are positive or non-negative.

Here's a variant. Instead of integers, the coin has
a positive rational on each side.

Date Subject Author
1/30/13 William Elliot
1/30/13 forbisgaryg@gmail.com
1/31/13 William Elliot
2/1/13 forbisgaryg@gmail.com
2/1/13 Dan Heyman
1/30/13 David C. Ullrich
1/30/13 Steve Oakley
1/31/13 Paul
1/31/13 Frederick Williams
1/31/13 David Petry
2/1/13 Richard Tobin
2/1/13 David C. Ullrich
2/1/13 Paul
2/2/13 Jim Burns
2/2/13 Jim Burns
2/2/13 Paul
2/2/13 David C. Ullrich
2/2/13 David C. Ullrich
2/2/13 Paul
2/3/13 David C. Ullrich
1/31/13 Frederick Williams
1/31/13 Butch Malahide
1/31/13 JohnF
2/1/13 ArtflDodgr
2/1/13 Butch Malahide
2/2/13 William Elliot
2/2/13 Paul
2/3/13 quasi
2/3/13 Paul
2/3/13 Paul
2/3/13 quasi
2/3/13 quasi
2/3/13 Butch Malahide
2/6/13