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Geometric Probability
5.8
• Calculate geometric probabilities.
• Use geometric probability to predict results in real-world
situations.
Probability is the likelihood that an
event will happen..
If every outcome in the sample space is
equally likely, the theoretical probability
of an event is
Geometric Probability is probability with
length or area.
Use the Spinner to find the Probability
The pointer landing on yellow.
The angle measure in the
yellow region is 140°.
Use the Spinner to find the Probability
The pointer landing on blue or red.
The angle measure in the blue region is 52°.
The angle measure in the red region is 60°.
Use the Spinner to find the Probability
The pointer not landing on green.
The angle measure in the green region is 108°.
Subtract this angle measure from 360°.
Use the Spinner to find the Probability
The pointer landing on red or yellow.
The probability is
that the
spinner will land on red or
yellow.
Using Length to Find Geometric Probability
A point is chosen randomly on PS. Find the
probability of each event.
The point is on RS.
The point is not on QR.
The point is on PQ or QR.
P(PQ or QR) = P(PQ) + P(QR)
Using Length to Find Geometric Probability
Use the figure below to find the probability
that the point is on BD.
Using Length to Find Geometric Probability
A point is chosen randomly on EH. Find the
probability of each event.
a. The point is on EG.
3
5
b. The point is not on EF.
13
15
Using Length to Find Geometric Probability
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.
Walk
Don’t Walk
45 sec.
70 sec.
The signal is “WALK” for 45 out
of every 115 seconds.
Using Length to Find Geometric Probability
A traffic light is green for 25 seconds, yellow
for 5 seconds, and red for 30 seconds. What is
the probability that the light will not be on red
when you arrive?
The probability that the light will not be on red is
Using Length to Find Geometric Probability
You are visiting San Francisco and are taking a trolley ride to a store on
Market Street. You are supposed to meet a friend at a store at 3:00 PM The
trolley runs every 10 minutes and the trip to the store is 8 minutes. You
arrive at the trolley stop at 2:48 PM. What is the probability that you will
arrive at the store by 3:00 PM?
To begin find the greatest amount of time you can afford to wait for the trolley and still
get to the store by 3 PM.
Because the ride takes 8 minutes, you need to catch the trolley no later than 8 minutes
before 3PM, or by 2:52 PM.
Using Area to Find Geometric Probability
If a dart hits the board below, find the
probability that it will land in the
shaded region.
Divide into equal parts.
2 1

8 4
Using Area to Find Geometric Probability
If a dart hits the board below, find the
probability that it will land in the shaded
region.
1
3
Using Area to Find Geometric Probability
A square game board consists of shaded and non-shaded
regions of equal width as shown. What is the chance that a dart
thrown at the board will land in a shaded area?
72
P(event) 
121
Using Area to Find Geometric Probability
A regular hexagon is inscribed in a circle with a diameter
of 12. Find the probability that a point chosen at random
lies in the shaded regions.
(Ao – A)  2
Ao
(r2 – ½aP)  2
r2
36
36
12
3 3
6
18 – 27 3
36
P.086 or 8.6%
Using Area to Find Geometric Probability
A game board consists of a circle inscribed in a
square. What is the chance that a dart thrown at the
board will land in the shaded area?
A – Ao
A
s2 – r2
s2
122 – 36
122
144 – 36
144
12
P .214 or 21.4%
Using Area to Find Geometric Probability
If a dart hits the board below, find the probability that it
will land in the shaded region.
A – 6Ao
A
lw – 6r2
lw
16  24 – 6  16
16  24
384 – 96
384
16
P .214 or 21.4%
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.
2A
P(A)=
A
200  .14
P(A)=
1400
A
A
P(A)= 
P(A )=
A
A
81  .18
450
P(A)=
 .32
P(A )=
1400
1400
Using Area to Find Geometric Probability
Find the probability that a point chosen randomly inside
the rectangle is not inside the circle or trapezoid. Round to
the nearest hundredth.
A – Ao – A
A
900 – 113.1 – 75
900
P .79 or 79%
Using Area to Find Geometric Probability
If a dart hits the board below, find the probability that it
will land in the shaded region.
A – A
A
S2 – s2
S2
52 – 32
52
25 – 9
25
P= .64 or 64%
Using Area to Find Geometric Probability
If a dart hits the board below, find the probability
that it will land in the shaded region.
A – Ao
A
R2 – r2
R2
9 – 4
9
5
9
5
9
P .556 or 55.6%
a. 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
b. Use the spinner to find the probability of the
pointer landing on a shaded area.
0.5
Find the probability that a point chosen
randomly inside the rectangle is in the triangle.
0.25
0.087
0.196
0.4
0.67
0.67
A Sunday night sports show is on from 10:00 p.m. to 10:30
p.m. You want to find out if your favorite team won this
weekend, but forgot that the show was on. You turn it on at
10:14 p.m. The score will be announced at one random
time during the show. What is the probability that you
haven’t missed the report about your favorite team?
0.53
0.6
0.47
0.5
0.07
0.82
0.33
1.00
Assignment
Geometric Probability