Geometric Probability 9-6 Geometric Probability Warm Up Lesson Presentation Lesson Quiz Holt Geometry

Lesson Quiz: Part I Describe the effect of each change on the area of the given figure. 1. The base length of the rectangle is multiplied by 8. The area is multiplied by 8. 2. The radius of the circle is tripled. The area is multiplied by 9.

Lesson Quiz: Part II 3. A square has an area of 49 cm2. If the area is quadrupled, what happens to the side length? The side length is doubled. 4. Rob had a 10 ft by 12 ft wall painted. For a wall twice as wide, the painter charged him twice as much. Is this reasonable? Explain. Yes; the second wall has twice the area of the first wall.

Find the area of each figure. 1. Warm Up Find the area of each figure. 1. 3. 3 points in the figure are chosen randomly. What is the probability that they are collinear? A = 36 ft2 2. 0.2 A = 20 m2

Objectives Calculate geometric probabilities. Use geometric probability to predict results in real-world situations.

Vocabulary geometric probability

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 of each event. The point is on RS.

Example 1B: Using Length to Find Geometric Probability The point is not on QR. Subtract from 1 to find the probability that the point is not on QR.

Example 1C: Using Length to Find Geometric Probability The point is on PQ or QR. P(PQ or QR) = P(PQ) + P(QR)

Check It Out! Example 1 Use the figure below to find the probability that the point is on BD.

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? To find the probability, draw a segment to represent the number of seconds that each signal is on. The signal is “WALK” for 45 out of every 115 seconds.

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. In the model, the event of stopping and waiting more than 40 seconds is represented by a segment that starts at B and ends 40 units from C. The probability of stopping and waiting more than 40 seconds is If you arrive at the light 40 times, you will probably stop and wait more than 40 seconds about (40) ≈ 10 times.

Check It Out! Example 2 Use the information below. What is the probability that the light will not be on red when you arrive? The probability that the light will be on red is

Example 3A: Using Angle Measures to Find Geometric Probability Use the spinner to find the probability of each event. the pointer landing on yellow The angle measure in the yellow region is 140°.

Example 3B: Using Angle Measures to Find Geometric Probability Use the spinner to find the probability of each event. the pointer landing on blue or red The angle measure in the blue region is 52°. The angle measure in the red region is 60°.

Example 3C: Using Angle Measures to Find Geometric Probability Use the spinner to find the probability of each event. the pointer not landing on green The angle measure in the green region is 108°. Subtract this angle measure from 360°.

Check It Out! Example 3 Use the spinner below to find the probability of the pointer landing on red or yellow. The probability is that the spinner will land on red or yellow.

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.

Example 4A: Using Area to find Geometric Probability the circle The area of the circle is A = r2 = (9)2 = 81 ≈ 254.5 ft2. The area of the rectangle is A = bh = 50(28) = 1400 ft2. The probability is P = 254.5 1400 ≈ 0.18.

Example 4B: Using Area to find Geometric Probability the trapezoid The area of the trapezoid is The area of the rectangle is A = bh = 50(28) = 1400 ft2. The probability is

Example 4C: Using Area to find Geometric Probability one of the two squares The area of the two squares is A = 2s2 = 2(10)2 = 200 ft2. The area of the rectangle is A = bh = 50(28) = 1400 ft2. The probability is

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. Area of rectangle: 900 m2 The probability of landing inside the triangle (and circle) and trapezoid is 0.29. Probability of not landing in these areas is 1 – 0.29 = 0.71.

Lesson Quiz: Part I A point is chosen randomly on EH. Find the probability of each event. 3 5 1. The point is on EG. 13 15 2. The point is not on EF.

Lesson Quiz: Part II 3. An antivirus program has the following cycle: scan: 15 min, display results: 5 min, sleep: 40 min. Find the probability that the program will be scanning when you arrive at the computer. 0.25 4. Use the spinner to find the probability of the pointer landing on a shaded area. 0.5

Lesson Quiz: Part III 5. Find the probability that a point chosen randomly inside the rectangle is in the triangle. 0.25