1. 5-Minute Check on Lesson 11-4 Transparency 11-5 Click the mouse button or press the Space Bar to display the answers. Find the area of each figure. Round to the nearest tenth if necessary. 1. 2. 3. 4. 5. Find the area of the figure 6. Find the figure’s area. Standardized Test Practice: ACB D 112 units²136.8 units²162.3 units² 212.5 units² A = 330 units² A = 12 units² C A = 117.7 units² A = 120 units² 14 10 8 12 8 8 3 15 14 A = 100.7 units²

2. Lesson 11-5 Geometric Probability

3. Objectives Solve problems involving geometric probability Solve problems involving sectors and segments of circles

4. Vocabulary Geometric Probability – probability involving geometric measure such as length or area Sector – of a circle is bounded by a central angle and its intercepted arc Segment – region of a circle bounded by and arc and a chord

5. Circles - Probability y x Radius (r) Diameter (d) Center Circumference = 2 πr = dπ 0° 180° 90° 270° 135° 315° Pie Charts Probability 0 = no chance 1 = for sure 135º ------ = 3/8 360º or.375 or 37.5% 180º ------ = 1/2 360º or.5 or 50% 45º ------ = 1/8 360º or.125 or 12.5%

6. Probability Area of Event ------------------ Total Area Radius (r) Center S T Probability Area of Event ¼ * πr 2 ------------------ = --------- Total Area πr 2 ¼ * πr 2 P(e) = --------- πr 2 ¼ = -------- = 0.25 1 0 ≤ P(e) ≤ 1 Event (e) Geometric Probability

7. Example 5-1a Grid-In Test Item 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? Read the Test Item You want to find the probability of landing in the shaded area, not the circle.

8. Example 5-1a Solve the Test Item We need to divide the area of the shaded region by the total area of the game board. The total area of the board is square inches. The area of the shaded region is the area of the total board minus the area of the circle. The area of the circle is The probability of throwing a dart onto the shaded area is or about 0.215.

9. Example 5-1b Grid In Test Item 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? Answer: 0.595

10. Example 5-2a Find the area of the shaded sectors. The shaded sectors have degree measures of 45 and 35 or 80° total. Use the formula to find the total area of the shaded sectors. Area of a sector Simplify. Answer:Area of the shaded sectors is 18 π or about 56.5 sq inches.

11. Example 5-2b Find the probability that a point chosen at random lies in the shaded region. To find the probability, divide the area of the shaded sectors by the area of the circle. The area of the circle is πr² with a radius of 9. Use a calculator. Simplify. Geometric probability formula Answer:The probability that a random point is in the shaded sectors is or about 0.22.

12. Example 5-2b Use a calculator. Simplify. Geometric probability formula Answer:The probability that a random point is in the shaded sectors is or about 0.22.

13. Example 5-2c Answer: or about a. Find the area of the orange sectors. b. Find the probability that a point chosen at random lies in the orange region. Answer: or about 0.33

14. Summary & Homework Summary: –To find geometric probability, divide the area of a part of a figure by the total area Homework: –pg 625-627; 10-15