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Geometric Probability Chapter 9 – Lesson 6 Geometric Probability
Objective: The students will calculate geometric probabilities and use geometric probability to predict results in real-world situations.
Vocabulary geometric probability
Any set of outcomes is called an event. Remember that in probability, the set of all possible outcomes of an experiment is called the sample space. Any set of outcomes is called an event. If every outcome in the sample space is equally likely, the theoretical probability of an event is
Geometric probability is used when an experiment has an infinite number of outcomes. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area. The outcomes of an experiment may be points on a segment or in a plane figure.
If an event has a probability p of occurring, the probability of the event not occurring is 1 – p. Remember!
Example 1A: Using Length to Find Geometric Probability A point is chosen randomly on PS. Find the probability the point is on RS.
Example 1B: Using Length to Find Geometric Probability A point is chosen randomly on PS. Find the probability the point is not on QR.
Example 1C: Using Length to Find Geometric Probability A point is chosen randomly on PS. Find the probability the point is on PQ or QR. P
Example 2A: Transportation Application A pedestrian signal at a crosswalk has the following cycle: “WALK” for 45 seconds and “DON’T WALK” for 70 seconds. What is the probability the signal will show “WALK” when you arrive? 70 45
Example 2B: Transportation Application If you arrive at the signal 40 times, predict about how many times you will have to stop and wait more than 40 seconds. P 30 40
Example 3A: Using Angle Measures to Find Geometric Probability Use the spinner to find the probability of the pointer landing on yellow.
Example 3B: Using Angle Measures to Find Geometric Probability Use the spinner to find the probability of the pointer landing on blue or red .
Example 3C: Using Angle Measures to Find Geometric Probability Use the spinner to find the probability of the pointer not landing on green.
Example 4: Using Area to find Geometric Probability Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. Circle Trapezoid One of two squares
Check It Out! Example 4 Find the probability that a point chosen randomly inside the rectangle is not inside the triangle, circle, or trapezoid. Round to the nearest hundredth.
Lesson Summary: Objective: The students will calculate geometric probabilities and use geometric probability to predict results in real-world situations.
Preview of the Next Lesson: Objective: The students will complete a practice test on Chapter 9.
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