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:
· 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?
Lesson Overview:
· 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, hop-scotch, skeet ball, etc. Games where geometric probability occur. 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?
· How can you support a conclusion that you make?
· Use resources from your building.
EALRs/GLEs:
1.4.1
1.4.2
3.1.1
3.2.2
I tem Specification s: PS01; SR02; SR04
Assessment:
· Use WASL format items that link to what is being covered by the classroom activity
· Include multiple choice questions
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 (consider one-dart play only)? 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.
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4. There is a circular dartboard. It costs $2.00 to throw a dart. You win $4.00 if you hit the square outside of the circle. 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”
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5. A dart hits the board. Which is the probability that it will hit in region II?
O A.
O B.
O C.
O D.