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11.5 Geometric Probability

11.5 Geometric Probability. Objectives. What is Geometric Probability? What is a sector of a circle? How to find the area of a sector of a circle? How to find the area of a segment of a circle?. What is Geometric Probability?.

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11.5 Geometric Probability

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  1. 11.5Geometric Probability

  2. Objectives • What is Geometric Probability? • What is a sector of a circle? • How to find the area of a sector of a circle? • How to find the area of a segment of a circle?

  3. What is Geometric Probability? • Probability that involves a geometric measure such as length or area is called Geometric Probability. If a point in region A is chosen at random, then the probability P(B) that the point is in region B, which is in the interior of region A, is P(B)= Area of region B Area of region A A B

  4. Probability With Area 8 B 22 18 A 46 P(A)= Area of region A Area of region B P(A)= 18 ∙ 8 46∙ 22 P(A)= .14 ~Simplify

  5. What is a sector of a circle? A sector of a circle is a region of a circle bounded by a central angle and its intercepted arc. Central Angle Arc Sector

  6. Formula to find area of a Sector of a Circle If a sector of a circle has an area of A square units, a central angle measuring N°, and a radius of r units, then A = (N/360)·πr² r N°

  7. How to find the area of a sector? Interior Angle= 50 Interior Angle= 65 18 Interior Angle= 62 Interior Angle= 77 Find the area of 2010’s sales. 2 Area of any section= interior angle of section radius 360 2 A= 62 9 ~Radius= 9 Interior angle of 2010’s sales= 62 360 2 A= 43.8 units ~ Simplify

  8. Probability With Sectors Interior Angle of Section A = 80 Interior Angle of Section B = 57 Interior Angle of Section C = 57 Interior Angle of Section D = 46 Interior Angle of Section E = 50 Interior Angle of Section F = 70 F A E B C D Find the probability that a point chosen randomly will land in section E. 2 Area of any section= interior angle of section radius 360 2 50 A= 8 ~ Radius=8 Interior angle of section E= 50 360 Area= 8.9 ~ Simplify Probability of any section= Area of section Area of circle 2 Probability of section E=8.9 ~ Area of section E= 8.9 Area of circle= 8 2 8 Probability of section E= 0.14 or 14%

  9. What is a segment of a circle? The region of a circle bounded by an arc and a chord is called a segment of a circle. Chord Arc Segment

  10. Probability With Segments A regular Hexagon is inscribed in a circle with a diameter of 14.What is the Probability that a point chosen randomly will land in segment A? A Area of the Sector: A= (N/360)·πr² =(60/360)·π(7²) =49π/6 =25.66 Area Of the triangle: Since the regular hexagon is inscribe in a circle the triangle is Equilateral, with each side 7 units long. Use Properties of 30°-60°-90° triangles to find the Apothem. The Apothem is 6.06. 14 7

  11. Probability With Segments Find Area of Triangle: A=1/2bh =1/2(7)(6.06) =21.22 Area of Segment = area of sector – area of triangle = 25.66 – 21.22 = 4.44 Find the probability: P(A) = Area of segment/Area of Circle = 4.44/153.94 = 0.03 The probability that a point, randomly selected, would land on segment A is about .03 or 3% A 14 7

  12. Assignment • Pre-AP Geometry: Pgs. 625-627 #7-31 • Geometry: Pg 625 #7 - 23

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