1. Geometric Probability
LESSON 13–3
Geometric Probability

2. Five-Minute Check (over Lesson 13–2) TEKS Then/Now New Vocabulary
Key Concept: Length Probability Ratio
Example 1: Use Lengths to Find Geometric Probability
Example 2: Real-World Example: Model Real-World Probabilities
Key Concept: Area Probability Ratio
Example 3: Real-World Example: Use Area to Find Geometric Probability
Example 4: Use Angle Measures to Find Geometric Probability
Lesson Menu

3. From the 15 members of the prom committee, two will be chosen as chairman and treasurer. What is the probability that Julia and her friend Marco will be randomly selected as chairman and treasurer in that order? A. B. C. D.
5-Minute Check 1

4. A gym class is separated into teams of 8 students
A gym class is separated into teams of 8 students. Each team then randomly assigns the positions of captain and scorekeeper. What is the probability that Tina and Frank are selected for either position on their team? A. B. C. D.
5-Minute Check 2

5. Rico is choosing a password for his bank account from the letters of his last name: H-E-R-R-E-R-A. If he selects from the letters at random, what is the probability that the password will be his last name (Herrera)? A. B. C. D.
5-Minute Check 3

6. Mrs. Henderson is choosing groups of 3 students from her math class of 24 students. If the groups are randomly chosen, what is the probability that Jacob, Terrence, and Todd are in a group? A. B. C. D.
5-Minute Check 4

7. Mathematical Processes G.1(B), G.1(E)
Targeted TEKS
G.13(B) Determine probabilities based on area to solve contextual problems.
Mathematical Processes
G.1(B), G.1(E)
TEKS

8. You found probabilities of simple events.
Find probabilities by using length.
Find probabilities by using area.
Then/Now

9. geometric probability
Vocabulary

10. Concept

11. Length probability ratio
Use Lengths to Find Geometric Probability
Point Z is chosen at random on AD. Find the probability that Z is on AB.
Length probability ratio
Substitution
Answer: The probability that Z is on AB is , approximately 0.18, or approximately 18%.
Example 1

12. Point R is chosen at random on LO. Find the probability that R is on MN.
Example 1

13. Model Real-World Probabilities
ORBITS Halley’s Comet orbits the earth every 76 years. What is the probability that Halley’s Comet will complete an orbit within the next decade?
We can use a number line to model this situation. Since the comet orbits every 76 years, it will orbit again in 76 years or less. On the number line below, the event of an orbit in the next 10 years is modeled by EF.
Example 2

14. Find the probability of this event. Length probability ratio
Model Real-World Probabilities
Find the probability of this event.
Length probability ratio
EF = 10 and EG = 76
Simplify.
Answer: , approximately 0.13, or approximately 13%
Example 2

15. SUBWAY You are in the underground station waiting for the next subway car, and are unsure how long ago the last one left. You do know that the subway comes every sixteen minutes. What is the probability that you will get picked up in the next 12 minutes?
A. B.
C. D.
Example 2

16. Concept

17. Use Area to Find Geometric Probability
DARTS The targets of a dartboard are formed by 3 concentric circles. If the diameter of the center circle is 4 inches and the circles are spread 3 inches apart, what is the probability that a player will throw a dart into the center circle?
You need to find the ratio of the area of the center circle to the area of the entire dartboard. The radius of the center circle is 4 ÷ 2 or 2 inches, while the radius of the dartboard is or 8 inches.
Example 3

18. Area probability ratio
Use Area to Find Geometric Probability
Area probability ratio
A = πr 2
Simplify.
Answer: The probability that the dart hits in the center circle is or about 6%.
Example 3

19. RING TOSS If at a carnival, you toss a ring and it lands in the red circle shown below, then you win a prize. The diameter of the circle is 4 feet. If the dimensions of the blue table are 8 feet by 5 feet, what is the probability if the ring is thrown at random that you will win a prize?
A. about 31%
B. about 33%
C. about 35%
D. about 37%
Example 3

20. A. Use the spinner to find P(pointer landing on section 3).
Use Angle Measures to Find Geometric Probability
A. Use the spinner to find P(pointer landing on section 3).
The angle measure of section 3 is 122°.
P(pointer landing on section 3) =
Answer: The probability of landing on section 3 is approximately 34%.
Example 4

21. B. Use the spinner to find P(pointer landing on section 1).
Use Angle Measures to Find Geometric Probability
B. Use the spinner to find P(pointer landing on section 1).
The angle measure of section 1 is 26°.
P(pointer landing on section 1) =
Answer: The probability of landing on section 1 is approximately 7%.
Example 4

22. A. Use the spinner to find P(pointer landing on section C).
A. about 17%
B. about 16%
C. about 18%
D. about 27%
Example 4

23. B. Use the spinner to find P(pointer landing on section E).
A. about 24%
B. about 26%
C. about 27%
D. about 38%
Example 4

24. Geometric Probability
LESSON 13–3
Geometric Probability