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Geometric Probability
The student is able to (I can):
• Calculate geometric probabilites
• Use geometric probability to predict results in real-world
situations
theoretical probability If every outcome in a sample space is
equally likely to occur, then the theoretical
probability of an event is
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.
=
number of outcomes in the event
P
number of outcomes in the sample space
Examples: A point is chosen randomly on . Find the
probability of each event.
1. The point is on .
2. The point is not on .
RD
•
•
D
A
E
R
4 3 5
RA
RA
P
RD
=
7
12
=
RE
( ) ( )
not 1
P RE P RE
= − 1
RE
RD
= −
4
1
12
= −
8 2
12 3
= =
Examples
A stoplight has the following cycle: green for 25 seconds,
yellow for 5 seconds, and red for 30 seconds.
1. What is the probability that the light will be yellow when
you arrive?
5
60
P =
1
12
=
2. If you arrive at the light 50 times, predict about how
many times you will have to wait more than 10 seconds.
Therefore, if you arrive at the light 50 times, you will
probably stop and wait more than 10 seconds about
•
10
E
20
CE
P
AD
=
20
60
=
1
3
=
( )
1
50 17 times
3

Use the spinner to find the probability of each event.
1. Landing on red
2. Landing on purple or blue
3. Not landing on yellow
80
360
P =
2
9
=
75 60
360
+
=
P
135
360
=
3
8
=
360 100
360
−
=
P
260
360
=
13
18
=
Examples
Find the probability that a point chosen randomly inside the
rectangle is in each shape. Round to the nearest hundredth.
1. The circle
circle
rectangle
=
P
( )
( )( )
2
9
28 50

= 0.18

Examples
2. The trapezoid
trapezoid
rectangle
=
P
( )( )
( )( )
1
18 16 34
2
28 50
+
=
450
1400
= 0.32

Examples
3. One of the two squares
2 squares
rectangle
=
P
( )
( )( )
2
2 10
28 50
=
200
1400
= 0.14


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13.1 Geometric Probability

  • 1. Geometric Probability The student is able to (I can): • Calculate geometric probabilites • Use geometric probability to predict results in real-world situations
  • 2. theoretical probability If every outcome in a sample space is equally likely to occur, then the theoretical probability of an event is 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. = number of outcomes in the event P number of outcomes in the sample space
  • 3. Examples: A point is chosen randomly on . Find the probability of each event. 1. The point is on . 2. The point is not on . RD • • D A E R 4 3 5 RA RA P RD = 7 12 = RE ( ) ( ) not 1 P RE P RE = − 1 RE RD = − 4 1 12 = − 8 2 12 3 = =
  • 4. Examples A stoplight has the following cycle: green for 25 seconds, yellow for 5 seconds, and red for 30 seconds. 1. What is the probability that the light will be yellow when you arrive? 5 60 P = 1 12 =
  • 5. 2. If you arrive at the light 50 times, predict about how many times you will have to wait more than 10 seconds. Therefore, if you arrive at the light 50 times, you will probably stop and wait more than 10 seconds about • 10 E 20 CE P AD = 20 60 = 1 3 = ( ) 1 50 17 times 3 
  • 6. Use the spinner to find the probability of each event. 1. Landing on red 2. Landing on purple or blue 3. Not landing on yellow 80 360 P = 2 9 = 75 60 360 + = P 135 360 = 3 8 = 360 100 360 − = P 260 360 = 13 18 =
  • 7. Examples Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. 1. The circle circle rectangle = P ( ) ( )( ) 2 9 28 50  = 0.18 
  • 8. Examples 2. The trapezoid trapezoid rectangle = P ( )( ) ( )( ) 1 18 16 34 2 28 50 + = 450 1400 = 0.32 
  • 9. Examples 3. One of the two squares 2 squares rectangle = P ( ) ( )( ) 2 2 10 28 50 = 200 1400 = 0.14 