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?
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 =