document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #466954 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Hint:
\n" ); document.write( "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).
\n" ); document.write( "or
\n" ); document.write( "You can place the $\"n-1\"$ points using a coin toss.
\n" ); document.write( "If a semi-circle covering all $\"n\"$ points, indeed exists, then, a semi-circle covering
\n" ); document.write( "all $\"n\"$ points and starting from one of the points in a clock-wise direction also exists.\r
\n" ); document.write( "\n" ); document.write( "So, given a semi-circle which starts at one of the point in clock-wise direction.
\n" ); document.write( "The probability that the rest of the $\"n-1\"$ points will be in that semi-circle is \r
\n" ); document.write( "\n" ); document.write( " $\"1%2F%282%5E%28n-1%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "and for $\"n\"$ such semi-circle, the probability will be \r
\n" ); document.write( "\n" ); document.write( " $\"n%2F%282%5E%28n-1%29%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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