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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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Some Thoughts re: Bertrand problem - paradox | Comment 50 of 51 |
(In reply to Bertrand problem - paradox by luminita)

The Bertrand paradox used a variation of this problem to show that probabilities may not be well defined if the mechanism or method that produced the random variable is not clearly defined. 

Bertrand gave three arguments. Each seemingly valid, yet each also yielding a different result: (1) The 'random endpoints' method, (2) the "random radius" method, and (3) the "random midpoint" method.

Edwin Jaynes provided a solution to the seeming paradox using
the "maximum ignorance" principle and showed that neither (1) nor (3) complied with the unspoken requirement that the method need be scale and translation invariant. Only method (2) fit this criteria.

Using the "random radius" method, the solution given by np_rt is the correct one. The probability that a randomly drawn chord will be longer than the radius is SQRT(3)/2.

Edited on June 15, 2013, 7:33 am
  Posted by Dej Mar on 2013-06-15 07:31:58

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