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For my probability class I was given the following problem:

"There is a dart game where each region of the dart board is given a value. Assume that the dart will always hit in the scoring region and that all possible places in the scoring region of the dart board are equally likely. Find the distribution of possible scores that you can make on a single throw, using a credible source to get the dimensions."

The way I instinctively want to solve this is to find the area of each scoring zone and use the ratio of this area to total area to set up the score distribution. Is the correct way of going about this problem or is there a better way?

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    Area computation is fine. You will have to get official dartboard specifications from some standard source. Things will be a little inexact, because the thickness of the steel wires varies a bit. There are also differences in numerical values assigned, depending on whether it is, for example, English Darts or American darts. Of course the assumption that any region of area $A$ is just as likely to be hit as any other region of area $A$ is unreasonable, but that's what you have been asked to assume.2012-02-22

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