Re: Probability of picking a positive rational number at random

On Mar 14, 8:32 am, S_Pa...@xxxxxxxxxxx wrote:


At the bottum of this link:http://en.wikipedia.org/wiki/Coprime
This distribution is used to determine that the probability of two
random integers being coprime is 6/pi^2
If the distribution is not valid, how was it used to obtain this
result?

It's explained in the last paragraph on that page: "There is often
confusion about what a "randomly chosen integer" is. One way of
understanding this is to assume that the integers are chosen randomly
between 1 and an integer N. Then for each upper bound N, there is a
probability P_N that two randomly chosen numbers are coprime. This
will never be exactly 6/pi^2, but in the limit as N goes to infinity,
P_N goes to 6/pi^2."

You can get answers to some problems with this trick but you must be
careful when changing the order of taking limits. So with your problem
(if I understand correctly) you would have to consider rational
numbers where both numerator and denominator are bounded by N and, if
you can get an answer for that problem, see if taking the limit as N
goes to infinity makes sense for your original problem.
.

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