What is Geometric Probability?
**Geometric Probability** is a way of calculating probability using geometric measurements like length, area, or volume. Instead of counting outcomes like a coin flip or die roll, we're looking at the ratio of favorable space to total space.
The basic formula is:
$$P(\text{event}) = \frac{\text{Measure of favorable space}}{\text{Measure of total space}}$$
For example, if you drop a coin onto a square target, the probability of it landing in a small circular area inside is the ratio of the circle's area to the square's area.
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Video: The Dartboard Analogy!
Watch this video to visualize how geometric probability works with a dartboard! π―
Practice Problems
Calculate the geometric probability for each scenario. Round to two decimal places.
1) A point is randomly chosen on a line segment of length 10. What is the probability it is on a segment of length 2?
2) A dart hits a circular target of radius 10. The bullseye has a radius of 2. What is the probability of hitting the bullseye? (Use Ο=3.14)
3) A point is randomly chosen inside a square with side length 5. What is the probability it is in a small square of side length 1 inside the bigger one?
4) A point is in a circle of radius 4. What is the probability it is in a sector with a central angle of $90^\circ$?
β‘ Geometric Probability Speed Quiz
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