Five pins are randomly nailed to a square board (according to a uniform probability distribution), and a rubber band is stretched completely around them to form a convex shape.
What is the probability that the rubber band is in the shape of a quadrilateral?
(In reply to
No Subject by Charlie)
To see what the stats would be if the original area for the randomized points were a circular disk rather than a square the selection criteria were added that points outside the circle would not be chosen, leaving the randomization uniform, via:
for i=1:5
x(i)=-10;
while (x(i)-.5)^2+(y(i)-.5)^2>.25
x(i)=rand; y(i)=rand;
end
end
The statistics were:
cts =
0 0 9499303 54885616 35615081
trial =
100000000
ans =
0 0 0.09499303 0.54885616 0.35615081
triangle 9.50 %
quadrilateral 54.89 %
pentagon 35.62 %
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Posted by Charlie
on 2023-09-27 22:17:10 |
If the randomization area were a circle rather than a square
