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Probability to find a great circle touching at least K points on a sphere, given N randomly drawn points
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N points are randomly drawn with a pen on a sphere. The thickness of the pen is of that size that for a great circle drawn on the sphere the probability that a randomly drawn point touches it is p. What is the probability to be able to draw a great circle on the sphere which touches at least K points?
I need this probability estimation (with N=100, K=10, p=1/100) for a historic discussion about whether it is a coincidence that on the great circle through Giza and Easter Island (thickness 1 degree) there are more than 10 important prehistoric monuments.
probability
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
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add a comment |
$begingroup$
N points are randomly drawn with a pen on a sphere. The thickness of the pen is of that size that for a great circle drawn on the sphere the probability that a randomly drawn point touches it is p. What is the probability to be able to draw a great circle on the sphere which touches at least K points?
I need this probability estimation (with N=100, K=10, p=1/100) for a historic discussion about whether it is a coincidence that on the great circle through Giza and Easter Island (thickness 1 degree) there are more than 10 important prehistoric monuments.
probability
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
$endgroup$
$begingroup$
I think a solution does not involve any geometry. The question sounds like geometry but it is pure probability/combinatorics.
$endgroup$
– Bernd Borchert
Jan 3 at 13:56
add a comment |
$begingroup$
N points are randomly drawn with a pen on a sphere. The thickness of the pen is of that size that for a great circle drawn on the sphere the probability that a randomly drawn point touches it is p. What is the probability to be able to draw a great circle on the sphere which touches at least K points?
I need this probability estimation (with N=100, K=10, p=1/100) for a historic discussion about whether it is a coincidence that on the great circle through Giza and Easter Island (thickness 1 degree) there are more than 10 important prehistoric monuments.
probability
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
$endgroup$
N points are randomly drawn with a pen on a sphere. The thickness of the pen is of that size that for a great circle drawn on the sphere the probability that a randomly drawn point touches it is p. What is the probability to be able to draw a great circle on the sphere which touches at least K points?
I need this probability estimation (with N=100, K=10, p=1/100) for a historic discussion about whether it is a coincidence that on the great circle through Giza and Easter Island (thickness 1 degree) there are more than 10 important prehistoric monuments.
probability
probability
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
asked Jan 3 at 8:53
Bernd BorchertBernd Borchert
112
112
$begingroup$
I think a solution does not involve any geometry. The question sounds like geometry but it is pure probability/combinatorics.
$endgroup$
– Bernd Borchert
Jan 3 at 13:56
add a comment |
$begingroup$
I think a solution does not involve any geometry. The question sounds like geometry but it is pure probability/combinatorics.
$endgroup$
– Bernd Borchert
Jan 3 at 13:56
$begingroup$
I think a solution does not involve any geometry. The question sounds like geometry but it is pure probability/combinatorics.
$endgroup$
– Bernd Borchert
Jan 3 at 13:56
$begingroup$
I think a solution does not involve any geometry. The question sounds like geometry but it is pure probability/combinatorics.
$endgroup$
– Bernd Borchert
Jan 3 at 13:56
add a comment |
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$begingroup$
I think a solution does not involve any geometry. The question sounds like geometry but it is pure probability/combinatorics.
$endgroup$
– Bernd Borchert
Jan 3 at 13:56