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eigenschmeigen

n points are placed at random on the circumference of a circle, what is the probability that they all lie within a common semicircle?

  • 2 years ago
  • 2 years ago

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  1. satellite73
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    i have googled this question and there are many explanations, but i have to say i don't even really understand what it is asking

    • 2 years ago
  2. eigenschmeigen
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    think of placing points at random, now what is the probability that it is possible to cut the circle in half leaving all the points on one side, for example it is possible here: |dw:1333717099690:dw|but not here:|dw:1333717241684:dw|

    • 2 years ago
  3. UnkleRhaukus
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    if n=2 P=1 if n>3 P<1 ....

    • 2 years ago
  4. UnkleRhaukus
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    \[P(n)\]

    • 2 years ago
  5. eigenschmeigen
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    ill post my thoughts so far.

    • 2 years ago
  6. eigenschmeigen
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    trivially P(1) = 1

    • 2 years ago
  7. UnkleRhaukus
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    this question reminds me of Buffon's needle problem

    • 2 years ago
  8. eigenschmeigen
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    P(2) is also easy, but we can learn from it: 1 point, A is already there, so placing another point the only place which is questionable is 180 degrees from A , i dont know whether it counts but it doesnt matter as the probability of that position exactly is 0 , therefore P(2) =1

    • 2 years ago
  9. eigenschmeigen
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    now for three points

    • 2 years ago
  10. UnkleRhaukus
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    is P(3)=1/2?

    • 2 years ago
  11. UnkleRhaukus
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    the first two points are in the same semi circle always , the third is either in-between the or out-between them, equal chance/?

    • 2 years ago
  12. eigenschmeigen
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    yes i think so! maybe.. |dw:1333724818545:dw|

    • 2 years ago
  13. eigenschmeigen
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    placing C on the circle somewhere.. where is allowed?

    • 2 years ago
  14. eigenschmeigen
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    maybe its not 1/2 ...

    • 2 years ago
  15. UnkleRhaukus
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    1/2 in the worst case scenario, ie if the first two points are opposite

    • 2 years ago
  16. eigenschmeigen
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    |dw:1333725166177:dw| i think its \[\frac{l}{(circumference)}\]

    • 2 years ago
  17. eigenschmeigen
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    those lines from A and B are diameters

    • 2 years ago
  18. UnkleRhaukus
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    this is a good question . and i can see you are getting closer and closer, but for now i must go (you might want to check out the Buffon's needle problem for some hints

    • 2 years ago
  19. eigenschmeigen
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    thanks for the help

    • 2 years ago
  20. rym
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    50 percent

    • 2 years ago
  21. TuringTest
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    I agree, good question This is perhaps a good question for the meta-math section

    • 2 years ago
  22. eigenschmeigen
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    to anyone viewing i think (guessing) maybe i should find l in terms of theta , then use an integral to find P(theta from A diameter)

    • 2 years ago
  23. eigenschmeigen
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    whats the meta math section?

    • 2 years ago
  24. TuringTest
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    click the "mathematics" blue bar you will see it is a category

    • 2 years ago
  25. TuringTest
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    http://openstudy.com/study#/groups/Meta-math

    • 2 years ago
  26. TuringTest
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    hard and irregular questions are found and solved there

    • 2 years ago
  27. eigenschmeigen
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    oh cool

    • 2 years ago
  28. TuringTest
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    but it can take a long time to get a response in that section, so take your pick keep "bumping" it here, or post in meta-math and wait...

    • 2 years ago
  29. eigenschmeigen
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    or both? hehe

    • 2 years ago
  30. TuringTest
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    in the meantime let me call on some who may be able to solve this: @across @JamesJ @Zarkon @Mr.Math @FoolForMath interesting probability problem (none are online right now it seems)

    • 2 years ago
  31. TuringTest
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    I'm not sure if you can post in both sections with the new "bump" system, but feel free to try :)

    • 2 years ago
  32. TuringTest
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    oh, mr.math is here after all maybe he has some nice thoughts on this

    • 2 years ago
  33. Mr.Math
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    I found this http://mathproblems.info/images/prob1.pdf

    • 2 years ago
  34. FoolForMath
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    I liked this answer: http://math.stackexchange.com/a/18371/2109

    • 2 years ago
  35. TuringTest
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    I can almost understand the MSE one, but I can't read Mr.Math's answer... when will my brain grow up like that?

    • 2 years ago
  36. TuringTest
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    I can see how they're kinda the same...

    • 2 years ago
  37. eigenschmeigen
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    i understand FFMs but i am struggling with mr.maths , i understand what's going on in general, im just not following all of the maths there. i think i need more experience with continuous probability and expected values..

    • 2 years ago
  38. eigenschmeigen
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    gonna close it up now unless anyone has more to add, thanks guys for all your help :)

    • 2 years ago
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