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Geometry – Chapter 14 Day #6
Topic: Geometric Probability
Standards/Goals:
 A.1.f.: I can find the probability of a simple event.
 F.1.c.: I can use area to solve problems involving geometric probability.
Today, we’re going to use more properties from geometry (namely area) to find probabilities of
various events.
Examples:
̅̅̅̅ is chosen at random.
#1. Point O on 𝐴𝐷
What is the probability that O is on ̅̅̅̅
𝐵𝐶 ?
#2. Point P is on ̅̅̅
𝐹𝐽 is chosen at random.
̅̅̅̅?
What is the probability that P is on 𝐺𝐻
#3. A bus picks up passengers at a bus stop every 12 minutes in the morning. Suppose that Adrian
arrives at the bus stop at a random time. What is the probability that he will have to wait 5 minutes or
less for the next bus?
#4. A river runs every 40 minutes. If a passenger arrives at the ferry station at a random time, what is
the probability that he will have to wait at least 25 minutes for the ferry?
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#5. A regular octagon is inscribed in a square. A point P in
the square is chosen at random. What is the probability
that P lies in the shaded region?
#6. A circle is inscribed in a square. A point N in the square is chosen at random. What is the
probability that N lies in the shaded region?
#7. Suppose that a dart lands randomly on the target at the right. What is the probability that the dart
will land in the shaded region?
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̅̅̅̅ is on the given segment:
EXAMPLE: Find the probability that a point chosen at random from 𝑨𝑲
#1. ̅̅̅̅
𝐶𝐹
#2. ̅̅̅
𝐵𝐼
#3. ̅̅̅̅
𝐺𝐾
̅̅̅̅
#4. 𝐹𝐺
̅̅̅̅
#5. 𝐴𝐾
̅̅̅̅
#6. 𝐴𝐶
EXAMPLE: Use the dartboard shown for the next THREE questions. Assume that dart you throw will
land on the dartboard and is equally likely to land
at any point on the board.
#1. What is the probability of hitting region X?
#2. What is the probability of hitting region Y?
#3. What is the probability of hitting region Z?
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EXAMPLE: A point between A and B on each number line is chosen at random. What is the probability
that the point is between C and D?
#1.
#2.
#3.
#4.
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HOMEWORK – Chapter 14 Day #6
Name ____________________________________________________ Date_____
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