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 two-point 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 mid-point algorithm, on the other hand, will generate the desired result because every mid-point uniquely determines the chord itself, and each mid-point is uniformly generated.
Edited on October 26, 2004, 6:56 pm
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Posted by Bon
on 2004-10-26 18:54:02 |
re(2): You're right!
