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  "body": "\n## Summary\n\nGeometric probability studies random geometric objects, such as random points, lines or shapes in the plane or in space.\nIn the simplest case, a point is chosen uniformly in a region $\\Omega$ of finite positive area.\nThen the probability of a subregion $A$ is the area of $A$ divided by the area of $\\Omega$.\nClassic problems are [[Buffon's needle problem|06X5PF6YFP]] and the [[Bertrand paradox|0T0JWJ3M47]].\n\n## Remarks\n\nThe same rule works with length on a line and with volume in space.\nMathematicians studied such problems from the 17th century on. Their modern form is part of integral geometry and stochastic geometry.\n\n## Explanations\n\n### L1 human\n\nIn geometric probability you measure chances with lengths and areas instead of with counts.\nThrow a dart at random at a square board.\nThe chance to hit the inscribed circle is the area of the circle over the area of the square, that is $\\pi/4$.\n",
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