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Holt Geometry
9-6 Geometric Probability
Warm UpFind the area of each figure.
1. A = 36 ft2
A = 20 m22.
3. 3 points in the figure are chosen randomly. What is the probability that they are collinear?0.2
Holt Geometry
9-6 Geometric Probability
Calculate geometric probabilities.
Use geometric probability to predict results in real-world situations.
Objectives
Holt Geometry
9-6 Geometric Probability
1. Sample space is the set ofall possible outcomes of an experiment. Any set of outcomes is called an event.
2. The theoretical probability of an event is if every outcome in the sample space is equally likely= [ratio=]
Holt Geometry
9-6 Geometric Probability
3. Geometric probability is used when an experiment has an infinite number of outcomes.
4. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area.
Holt Geometry
9-6 Geometric Probability
(big)
(small)
Holt Geometry
9-6 Geometric Probability
A point is chosen randomly on PS. Find the probability of each event.
Example 1A: Using Length to Find Geometric Probability
A. The point is on RS.
B. The point is not on QR.
C. The point is on PQ or QR.
P(PQ or QR) = P(PQ) + P(QR)
Holt Geometry
9-6 Geometric Probability
A pedestrian signal at a crosswalk has the following cycle: “WALK” for 45 seconds and “DON’T WALK” for 70 seconds.
Example 2A: Transportation Application
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.
Holt Geometry
9-6 Geometric Probability
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.
Holt Geometry
9-6 Geometric Probability
Use the spinner to find the probability of each event.
Example 3A: Using Angle Measures to Find Geometric Probability
A. the pointer landing on yellow
b. the pointer landing on blue or red
c. the pointer not landing on green
Holt Geometry
9-6 Geometric Probability
Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth.
Example 4: 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 = 254.51400
≈ 0.18.
Holt Geometry
9-6 Geometric Probability
Example 4B: Using Area to find Geometric Probability
the trapezoid
The area of the rectangle is A = bh
= 50(28) = 1400 ft2.
The area of the trapezoid is
The probability is
Holt Geometry
9-6 Geometric Probability
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
Holt Geometry
9-6 Geometric Probability
Lesson Quiz: Part I
A point is chosen randomly on EH. Find the probability of each event.
1. The point is on EG.
2. The point is not on EF.
35
1315
Holt Geometry
9-6 Geometric Probability
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
Holt Geometry
9-6 Geometric Probability
Lesson Quiz: Part III
5. Find the probability that a point chosen randomly inside the rectangle is in the triangle.
0.25
Holt Geometry
9-6 Geometric Probability
HomeworkPg. 633
1-11, 20-30
EXTRA CREDIT Pg. 639-
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