SOLUTION: n points are located on the circumference of a given circle . What is the probability of all points are located on the same semi circle

Question 766503: n points are located on the circumference of a given circle . What is the probability of all points are located on the same semi circle
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Hint:
Start with a point randomly on the circle and draw a diameter from that point. All you got to do now is ensure that rest of the points lie on the same side of the diameter (i.e., on a semi-circle).
or
You can place the points using a coin toss.
If a semi-circle covering all points, indeed exists, then, a semi-circle covering
all points and starting from one of the points in a clock-wise direction also exists.
So, given a semi-circle which starts at one of the point in clock-wise direction.
The probability that the rest of the points will be in that semi-circle is

and for such semi-circle, the probability will be

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