Geometric Probability
When outcomes cannot be counted, probability becomes a ratio of measures. Favorable over total — applied to length, area, time and volume, with the pi cancelling whenever circles are involved.
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When outcomes cannot be counted, probability becomes a ratio of measures. Favorable over total — applied to length, area, time and volume, with the pi cancelling whenever circles are involved.
When outcomes cannot be counted one by one — a dart landing anywhere on a board, a train arriving at any moment — probability comes from a measure instead. Geometric probability is the favorable measure divided by the total measure.
The same idea covers any continuous measure — you just divide the part you want by the whole:
It assumes a uniform distribution — every point is equally likely.
The board has radius ; the target has radius . The cancels:
Waiting for a train (time)
A pond in a garden (area)
Four circles on a square board (area)
| Type | Formula | Example |
|---|---|---|
| Areas | area ÷ total area | a circle inside a rectangle |
| Lengths | length ÷ total length | a point on a segment |
| Times | time ÷ total time | train timetables |
| Volumes | volume ÷ total volume | a ball inside a box |