Pearson Unit 6 Topic 15: Probability 15-2: Geometric Probability Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (13)(B) Determine probabilities based on area to solve contextual problems. (1)(B) Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. (1)(E) Create and use representations to organize, record, and communicate mathematical ideas.

Geometric probability is used when an experiment has an infinite number of outcomes. In 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.

Formulas you should already know: Area of square: 𝐴= 𝑠 2 Area of rectangle: 𝐴=𝑏ℎ Area of triangle: 𝐴= 1 2 𝑏ℎ Area of trapezoid: 𝐴= 1 2 ℎ(𝑏 1 + 𝑏 2 ) Area of a circle: 𝐴=𝜋 𝑟 2

Example: 1 Find the probability it is on PQ. A point is chosen randomly on PS. Find the probability of each event. Find the probability it is on PQ. Find the probability it is on RS.

Example: 1 continued Find the probability it is on QR. A point is chosen randomly on PS. Find the probability of each event. Find the probability it is on QR. Find the probability it is on PR. Find the probability it is NOT on QR.

Example 2: A commuter train runs every 25 minutes, If a commuter arrives at the station at a random time, what is the probability that the commuter will have to wait at least 10 minutes for the train?

Example 2 continued A commuter train runs every 25 minutes, If a commuter arrives at the station at a random time, what is the probability that the commuter will have to wait at least 10 minutes for the train?

Example: 3 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? What is the probability the signal will show “DON’T WALK” when you arrive?

Answers for cycle: “WALK” for 45 seconds Example: 3 continued Answers for cycle: “WALK” for 45 seconds Answers for cycle: “DON’T WALK” for 70 sec.

Example: 4 Use the information below. What is the probability that the light will not be on red when you arrive?

Use the spinner to find the probability of each event. Example: 5 Use the spinner to find the probability of each event. Find the probability of the spinner landing on: Yellow Red Green or red Blue or red or yellow NOT green or blue

Example: 5 continued

Example: 6 In either of the two yellow squares In the circle Write the “plan” (do not actually compute using the numbers) to find the probability that a point chosen randomly inside the rectangle is in each shape. In either of the two yellow squares In the circle In the trapezoid In the green area (not in the yellow squares or the trapezoid)

Example: 6 continued

Example: 7 Find the probability that a point chosen randomly inside the rectangle is in the triangle.

Example: 7 continued

Example 8: An archery target has 5 colored scoring zones formed by concentric circles. The target’s diameter is 122 cm. The radius of the yellow zone is 12.2 cm. The width of each of the other zones is also 12.2 cm. If an arrow hits the target at a random point, what is the probability that it hits the red zone?

Example 8 continued An archery target has 5 colored scoring zones formed by concentric circles. The target’s diameter is 122 cm. The radius of the yellow zone is 12.2 cm. The width of each of the other zones is also 12.2 cm. If an arrow hits the target at a random point, what is the probability that it hits the red zone? P(arrow hits red zone) = 𝑟𝑒𝑑 𝑎𝑟𝑒𝑎 −𝑦𝑒𝑙𝑙𝑜𝑤 𝑎𝑟𝑒𝑎 𝑒𝑛𝑡𝑖𝑟𝑒 𝑡𝑎𝑟𝑔𝑒𝑡 𝑎𝑟𝑒𝑎