9.2.3 Geometric Probability
Key Objectives • Calculate geometric probabilities. • Use geometric probability to predict results in real-world situations. Key Terms • In geometric probability , the probability of an event is based on a ratio of geometric measures such as length or area.
Here are three models for geometric probability. In the length model, a point on a line is chosen at random within the sample space, which is the line segment AD . The event of interest is the choice of a point on the line segment BC . The probability of the event is equal to the ratio of the length of the event line segment to the length of the sample space line segment. In the angle measure model, a spinner is spun to choose an angle at random, or a dart is thrown to hit a point at random, within the sample space, which is all points in the circle. The event of interest is the choice of an angle or a point within the shaded region. The probability of the event is equal to the ratio of the measure of the central angle of the shaded region to 360°. In the area model, a point is chosen at random within the sample space, which is all the points in the area of a plane figure. The event of interest is the choice of a point within a plane figure inside the sample space, in this case a triangle. The probability of the event is equal to the ratio of the area of the smaller figure to the area of the sample space figure.
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