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Elizabeth Pawelka
Geometric Probability
4/11/12
Geometry
Lesson Plans
Section 7-8: Geometric Probability
4/11/12
Warm-up (15 mins)
Practice Workbook:
 Practice 7-6, # 15 – 23
 Practice 7-7, # 15 – 20
Find area of shaded segments. Round your answer to the nearest tenth.
p.1
Elizabeth Pawelka
Geometric Probability
4/11/12
p.2
Homework Review (10 mins) – ask for any questions on homework
Homework (H)
p. 397 # 1 - 11, 17 – 19, 22, 23, 25, 27, 32, 35
Homework (R)
p. 397 # 1 - 11, 17 – 19, 22, 25, 26, 27, 28, 35
Statement of Objectives (5 mins)
The student will be able to use area models to find probabilities of events.
Teacher Input (50 mins)

Probability: favorable outcomes
possible outcomes
If you had a six-sided number cube, what is the probability of rolling the following?
a. 4 (1/6)
b. an odd number (1/2)
c. 2 or 5 (1/3)
d. a prime number (1/2)
Elizabeth Pawelka

Geometric Probability
4/11/12
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Geometric Probability: model that uses points to represent outcomes; uses the ratio of the favorable
length, area, volume, etc. to the entire length, area or volume.
Finding Probability Using Segments
If a points of segments (line or time, etc.) represent outcomes, then:
P(event) = length of favorable segment
length of entire segment
Example 1: Segments
A point on segment AB below is selected at random. What is the probability that it is a point on
segment CD?
P( CD ) =
4 2
 = 40%
10 5
Example 2: Segments
Example 3: Time
Ashley’s bus runs every 25 minutes. If she arrives at her bus stop at a random time, what is the
probability that she will have to wait no more than 10 minutes for the bus?
Elizabeth Pawelka
Geometric Probability
4/11/12
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P(no more than 10 mins) = 10/25 = 2/5 = 40%
Example 4: Time
Finding Probability Using Area
If points of a region represent equally likely outcomes, you can find probabilities by comparing areas:
P(event) = area of favorable region
area of entire region
Elizabeth Pawelka
Example 5: Area
Geometric Probability
4/11/12
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Elizabeth Pawelka
Geometric Probability
4/11/12
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Example 6: Area - Dartboard
Assuming a dart you throw will land somewhere on this 1-ft square dartboard, what is the probability of
hitting the blue, yellow, and red areas? The radii of the concentric circles are 1, 2, and 3 inches.
P(blue) =
P(yellow) =
P(red) =
P(blue) = area of blue = π(12) π ≈ 0.022 or 2.2%
area of square 122
144
P(yellow) = area of yellow = π(22) - π(12) 4π - π = 3π ≈ 0.065 or 6.5%
area of square
122
144 144
P(red) = area of red = π(32) - π(22) 9π - 4π = 5π ≈ 0.109 or 10.9%
area of square
122
144
144
Example 7: Area – Coin Toss
Carnival Game of Coin Toss: To win, you must toss a quarter so it lands completely in the circle as
15
shown below. The circle has a 1 inch radius. The quarter has a
inch radius. Given that the coin
32
could land anywhere in the 8 inch square, what is the probability of winning?
P(winning) = area of 17/32 in circle (1 inch minus 15/32) = π(17/32)2 ≈ 0.014 or 1.4%
area of square
82
Elizabeth Pawelka
Geometric Probability
Closure (5 mins)
Today you learned to use area models to find probabilities of events.
Tomorrow we’ll review for the test on Friday.
Homework (H)
p. 404, # 1 – 9, 15 – 21, 23 – 25, 40 - 42
Homework (R)
p. 404, # 1 – 6, 15 – 18, 20, 21, 23 - 25
4/11/12
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