Download Geometric probability

9-6 Geometric Probability
Warm Up
Find the area of each figure.
1.
2.
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A = 36 ft2
A = 20 m2
3. 3 points in the
figure are chosen
randomly. What is
the probability that
they are collinear?
0.2
9-6 Geometric Probability
Objectives
Calculate geometric probabilities.
Use geometric probability to predict
results in real-world situations.
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9-6 Geometric Probability
1. Sample space is the set of
all 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=]
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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.
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9-6 Geometric Probability
(big)
(small)
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9-6 Geometric Probability
Example 1A: Using Length to Find Geometric Probability
A point is chosen randomly on PS. Find the
probability of each event.
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)
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9-6 Geometric Probability
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.
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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.
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9-6 Geometric Probability
Example 3A: Using Angle Measures to Find
Geometric Probability
Use the spinner to find the probability of each
event.
A. the pointer landing on yellow
b. the pointer landing on blue or red
c. the pointer not landing on green
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9-6 Geometric Probability
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.
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 =
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254.5 ≈ 0.18.
1400
9-6 Geometric Probability
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
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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
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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.
3
5
2. The point is not on EF.
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13
15
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
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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
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9-6 Geometric Probability
Homework
Pg. 633
1-11, 20-30
EXTRA CREDIT
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