Question 766503


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 {{{n-1}}} points lie on the same side of the diameter (i.e., on a semi-circle). 
or
You can place the {{{n-1}}} points using a coin toss. 
If a semi-circle covering all {{{n}}} points, indeed exists, then, a semi-circle covering 
all {{{n}}} 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 {{{n-1}}} points will be in that semi-circle is  

{{{1/(2^(n-1))}}}

and for {{{n}}} such semi-circle, the probability will be 

{{{n/(2^(n-1)) }}}