Wetenschap - 15 juni 1995

A common chance model

A common chance model

The tossing of a coin is usually represented as an example of a binomial chance distribution with p=1/2. When a die is thrown the six side planes get an apriori chance of exactly 1/6. We can generalize the first model to a cylinder (of a homogeneous kind of matter) with radius r and height h, and the second to a rectangular block with edges a, b and c respectively. Both bodies satisfy the requirement that its center of gravity lies on the normals that are raised in the center of gravity of each of the side planes. Furthermore the cylinder has two circles in common with a sphere with the centre in its centre of gravity, and the angular points of the rectangular block all lie on a sphere with the centre in its centre of gravity. Then the fractions of the chance distribution are proportional to the area of each part of the sphere that is related to a side plane, separated by the circles in case of the cylinder, and by the projections of the edges onto the sphere from its centre, in case
of the rectangular block.

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