On Wed, 30 Jan 2013, email@example.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.