GEOMETRIC PROBABILITY
Enduring Understanding: Develop a better understanding of how to identify, determine the size of,
or list the sample space and determine the probability of compound, dependent, and independent
events.
Essential Questions:
Original Lesson



How is geometric probability different
than theoretical probability?
How is a position defended or refuted by
using mathematical data?
How is the area of a region determined?
Suggestions for English Language Learners
Vocabulary:
Geometric probability
Theoretical probability
Defend
Refute
Sample spaces
Possible outcome
Lesson Overview:
Original Lesson
 Before allowing the students the
opportunity to start the activity: access
their prior knowledge with regards to
determining geometric probability.
Discuss with students the types of games
that they have played such as darts, hopscotch, skeet ball, etc., games where
geometric probability occurs. How many
students have gone bowling? How easy it
is the knock down a single pin? How
many have played or seen the games on
television?
 Review the terminology of “sample
spaces” and “possible outcomes”.
 Geometric probability can be described as
P(E) = measure of geometric model
representing desired outcomes in the event
measure of geometric model
representing all outcomes in the same space
 Link to the Star Problem that was done in
week 1.
 What is being asked by the questions in
the problem? How do you decode what
the problem is asking you to do?
 How can the students make their thinking
visible?
Suggestions for English Language Learners
 Show pictures of games with geometric
probability: bowling, darts, hopscotch.
Ask who has played these games.
Generate a list of other activities with
geometric probability, such as the TV
show Deal or No Deal.



How can you support a conclusion that
you make?
Use resources from your building.
NOTE: Question 4 is incomplete with
existing information.

Offer options of charts, graphs,
powerpoint
EALRs/GLEs:
1.4.1
1.4.2
3.1.1
3.2.2
Item Specifications: PS01; SR02; SR04
Assessment:
Original Lesson
 Use WASL format items that link to what
is being covered by the classroom activity
 Include multiple choice questions
Suggestions for English Language Learners
 Have students create a rubric to score the
activity.
Geometric Probability
Some examples of geometric measures are lengths, areas, angle measures and volumes.
1. A game at the state fair has a circular target with a radius of 10.7 cm on a square board measuring
30 cm on a side. Players win prizes if they throw a dart and hit the circular area only.
a. List the possible outcomes for a player throwing one dart.
b. List the possible outcomes if a player is throwing two darts.
c. What is the probability of a player winning with one dart? Remember to show all work.
(This answer is based on geometric probability)
d. Use your answer from c to answer this question: If 25 players were to play this game, how
many would you expect to win?
Support your answer using words, numbers and/or diagrams.
2. A tightrope approximately 320 m long is suspended between two poles. During a performance, a
break occurs in the line (the tightrope walker escapes without injury!). Assume that the line has an
equal chance of breaking anywhere along its length.
a. Draw a diagram for this problem and label.
b. Determine the probability that the break occurred in the first 50 m of the tight rope.
Support your answer using words, numbers and/or diagrams.
c. Determine the probability that the break occurred within 20 m of a pole.
Support your answer using words, numbers and/or diagrams.
3. During a special promotion at the Seattle Center, a bowling lane is set up. One blindfolded
contestant will roll a ball down a lane at a single pin. If the ball touches the pin, the contestant wins a
new car. The diameter of the bowling ball is 21.8 cm. The diameter of the pin is 10.2 cm. The lane
created is 101.6 cm wide. Side rails prevent the ball from leaving the lane.
a. Determine the possible outcomes in this situation.
b. The pin is placed in the middle of the lane. What is the probability that the ball will strike the
pin? Support your answer using words, numbers and/or diagrams.
c. The center has purchased an insurance policy that will pay for the car if the contestant wins.
To reduce the probability that the car is won, the insurance company suggests placing the pin at
the right-handed edge of the lane. Is the company correct? Defend your response.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
4. There is a circular dartboard. It costs $2.00 to throw a dart. You win $4.00 if you hit a square.
The radius of the circle is 5 inches. How long should the side of the square be made to make this
game fair? Support your answer using words, numbers and/or diagrams.
5”
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
5. If a dart randomly hits the board, what is the probability that it will hit in region II?
A.
9
20
B.
6
13
C.
1
4
D.
1
3
10”
30”
15”
I
II
10”
III
IV