What is the probability that a randomly drawn chord will be longer than the radius of the circle?
Prove it.
(In reply to
re: Different Approach (Continued) by Brian Smith)
It doesn't matter if you have 180 chords or 1800 chords, the number is still finite; we need to examine the entire infinite set of possible chords. As it turns out, as the number of chords approaches infinity, the probability approaches 2/3 (66.66...%).
The problem with this is assuming that the distribution of angles from a single point on the circumference is the same distribution of chords over the entire circle. In other words, you are assuming the same number of chords between 1° and 5° as between 76° and 80°, but how do you know that this is true for the entire infinite set of possible chords.
As Aaron pointed out, the chords closer to 0° and 180° are 'scrunched' together, while the chords around 90° are more spread out. That would seem to imply a different distrubution to accurately represent the entire range of possible chords.

Posted by DJ
on 20031015 12:17:35 