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Strike a Chord (..Any Chord) (Posted on 2003-10-09) Difficulty: 4 of 5
What is the probability that a randomly drawn chord will be longer than the radius of the circle?

Prove it.

No Solution Yet Submitted by DJ    
Rating: 4.5263 (19 votes)

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re: Both right, but... | Comment 5 of 51 |
(In reply to Both right, but... by Charlie)

I am not sure that I agree with Charlie's idea that the "randomness" of a particular method depends on their being some natural analogue of it (in fact, i would have suspected the opposite, in general). Nevertheless, he does have a point.

Imagine that we have a circular disk in 2-D space. then the answer given by myself and Bryan (fair enough- he got it first) corresponds to something like:

Given that we know cosmic ray X passed through point Y, but we know nothing about the angle of impact of the ray on the edge of the circle (and think that the angle of impact is random), what is the probability that the chord is greater in length than the radius.

np_rt's answer corresponds to something like:

Given that we know cosmic ray X passed through point Y on the diameter of the circle which is at a right angle to cosmic ray X, and we know nothing about where point Y is located on this diameter (and think that the location of Y on the diameter is random), what is the probability that the resulting chord is longer than the radius.

In other words, the different answers depend on different intepretations of what is random, either the angle at which the ray hits, or the point on the orthogonal diameter which it hits.
  Posted by RoyCook on 2003-10-09 15:54:03

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