What is the probability that a randomly drawn chord will be longer than the radius of the circle?
Prove it.
(In reply to
re: You're right! by Charlie)
Choosing two random points to form a chord is different from choosing a random chord though.
Imagine two chords, one if shorter than the other. Then using the twopoint method, the longer one has a higher chance than the shorter one, simply because the longer one cover more points.
However, the problem states that a random chord, implying each chord has the same probability being generated.
Your midpoint algorithm, on the other hand, will generate the desired result because every midpoint uniquely determines the chord itself, and each midpoint is uniformly generated.
Edited on October 26, 2004, 6:56 pm

Posted by Bon
on 20041026 18:54:02 