Re: I need FALSE PROOFS!!

From: Steve (sbrian1_at_houston.rr.com)
Date: 12/28/04 

Date: Tue, 28 Dec 2004 02:47:44 +0000 (UTC)

On 27 Dec 2004, Phil Carmody wrote:
>Alec McKenzie <mckenzie@despammed.com> writes:
>> sbrian1@houston.rr.com (Steve) wrote:
>>
>> > I heard this one from a systems analyst who refused to believe there was a
>> > flaw in it.
>> >
>> > The real numbers are written on two pieces of paper, one number on each. The
>> > papers are folded and placed in a box. One of the two is drawn out and read
>> > by someone ignorant of the values of the numbers. He is asked whether the
>> > other number, which we'll cal b, is larger or smaller than the one he has
>> > just read, which we'll call a. Can he improve his chance of success to above
>> > 50%?
>> >
>> > Yes. He should randomly select a real number, p. If p is greater than a,
>> > then he should guess that b is greater than a. If p is less than a, then he
>> > should guess that b is less than a. In other words, he should always guess
>> > that b is on the same side of a as p is.
>> >
>> > If p is between a and b, then the strategy works 100% of the time. If p is
>> > not between a and b, then it doesn't help, so the probability of guessing
>> > correctly remains at 50%. The overall probability of guessing correctly is
>> > then 50% + 100% times the probability that p is between a and b. The overall
>> > probability is clearly greater than 50%.
>>
>> Your systems analyst is correct: there is no flaw in it.
>>
>> However, the amount by which the chance of success is improved to above
>> 50% is very minute indeed, but not precisely zero.
>
>How much greater than zero?

Ostensibly by the probability that p is between a and b. Actually, of course, by 0, the above being a false proof.

Relevant Pages

  • Re: I need FALSE PROOFS!!
    ... Can he improve his chance of success to above ... > Your systems analyst is correct: there is no flaw in it. ... > 50% is very minute indeed, but not precisely zero. ...
    (sci.math)
  • Re: I need FALSE PROOFS!!
    ... Phil Carmody wrote: ... the amount by which the chance of success is improved to above ... A vanishingly small amount, perhaps? ...
    (sci.math)
  • Re: I need FALSE PROOFS!!
    ... the amount by which the chance of success is improved to ... >> above 50% is very minute indeed, but not precisely zero. ... > There is a slight flaw, though the probability remains above 50%. ...
    (sci.math)