The document discusses geometric probability, enabling students to calculate probabilities based on geometric measures such as length and area, with examples provided for real-world applications. It explains theoretical probability and includes practical scenarios like stoplight timing and spinner outcomes to predict results. Furthermore, it presents calculations for the probability of randomly chosen points within various geometric shapes.

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
