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Two people stand around a circular duck pond of radius R.  They are placed randomly along the circumference of the duck pond.  What is the probability that the distance between them is greater than R?

 Dec 5, 2019
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They will  be   R distance apart   whenever   we have  an equilateral triangle  with one vertex at the center of the circle and the other two vertexes  on the circle.......the sides will = R

 

And the  central angle  formed  by the two sides of R each will be 60°

 

So.....the probability  that the distance between them will  be  >  R  is given by

 

1 -  60/360   =

 

1  -  1/6  =

 

5/6

 

 

cool cool cool

 Dec 5, 2019

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