Introduction:
Problem A-6 of the 53rd Putnam Competition read as follows: “Four points are chosen at random on the surface of a sphere. What is the probability that the centre of the sphere lies inside the tetrahedron whose vertices are at the four points? (It is understood that each point is independently chosen relative to a uniform distribution on the sphere.)”(53rd Putnam, 1992, https://prase.cz/kalva/putnam.html) This paper will approach a way of generalising and attempting to use complex algorithms to determine the probability for any bi-dimensional convex shape. The algorithms, software used, mathematical definitions and equations used will be described more thoroughly throughout the paper.
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