The student is able to calculate geometric probabilities and use geometric probability to predict results in real-world situations. Geometric probability is based on a ratio of geometric measures such as length or area to calculate the probability of an event. Examples are provided to demonstrate calculating probabilities of events for points on lines and in plane figures, outcomes of experiments with spinners or stoplights, and areas of shapes within rectangles.

1. Obj. 48 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
P=
geometric
probability
number of outcomes in the event
number of outcomes in the sample space
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.

3. Examples
A point is chosen randomly on RD . Find the
probability of each event.
4
R
•
3
E
•
A
5
D
1. The point is on RA .
RA 7
P=
=
RD 12
2. The point is not on RE .
RE
P (not RE ) = 1 − P ( RE ) = 1 −
RD
4 8 2
= 1− = =
12 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?
P=
5
1
=
60 12

5. Examples
•
20
E 10
2. If you arrive at the light 50 times,
predict about how many times you will
have to wait more than 10 seconds.
CE 20 1
=
=
P=
AD 60 3
Therefore, if you arrive at the light 50
times, you will probably stop and wait
more than 10 seconds about
1
( 50 ) ≈ 17 times
3

6. Examples
Use the spinner to find the probability of
each event.
1. Landing on red
80 2
P=
=
360 9
2. Landing on purple or blue
75 + 60 135 3
P=
=
=
360
360 8
3. Not landing on yellow
360 − 100 260 13
P=
=
=
360
360 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
π ( 92 )
circle
P=
=
≈ 0.18
rec tangle ( 28 )( 50 )

8. Examples
2. The trapezoid
1
18 16 + 34 )
trapezoid 2 ( )(
=
P=
( 28 )( 50 )
rec tangle
=
450
≈ 0.32
1400

9. Examples
3. One of the two squares
2 ( 102 )
2 squares
=
P=
( 28 )( 50 )
rec tangle
=
200
≈ 0.14
1400