1. Geometric Probability
10-6
Geometric Probability
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Holt Geometry

2. Find the area of each figure. 1.
Warm Up
Find the area of each figure. 1.
10 in 3.
A = 36 ft2
A = 261 in2 2.
A = 20 m2

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

4. Vocabulary
geometric probability

5. 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

6. 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.

8. 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.

9. 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.
PQ + RS
7 + 5 12 = = PS 25 25

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

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

12. 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°.

13. 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°.

14. 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°.

15. 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.

16. 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.

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

18. the trapezoid
The area of the trapezoid is
The area of the rectangle is A = bh
= 50(28) = 1400 ft2.
The probability is

19. 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

20. 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.

21. Review:
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.

22. Review:
3. Use the spinner to find the probability of the pointer landing on a shaded area.
0.5
4. Find the probability that a point chosen randomly inside the rectangle is in the triangle.
0.25