Geometric Probability – Solve problems involving geometric probability – Solve problems involving sectors and segments of circles To win at darts, you.

Slides:



Advertisements
Similar presentations
Radius- Is the edge to the middle of the circle. Diameter- It goes throw the whole center of the circle.
Advertisements

Area of Polygons and Circles
GEOMETRY Circle Terminology.
Geometric Probability
11.5 Geometric probability By: Ryan Jacob and Brinley Mathew.
Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.
Circle Theorems-“No Brainers”
Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.
What do you mean? I Rule the World! Bulls eyeI’m on it! In-Mates and Ex-Cons S - words $ $ $ $ $ $ $ $
Geometric Probability.  Probability is the chance that something will happen.
Lesson 7.4B M.3.G.1 Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a particular ring on a dartboard.) M.3.G.2.
L.E.Q. How do you use segment and area models to find the probabilities of events?
Chapter 11 GRUDGE REVIEW.
Introduction A sector is the portion of a circle bounded by two radii and their intercepted arc. Previously, we thought of arc length as a fraction of.
Introduction Construction methods can also be used to construct figures in a circle. One figure that can be inscribed in a circle is a hexagon. Hexagons.
Constructing Regular Hexagons Inscribed in Circles Adapted from Walch Education.
Deriving the Formula for the Area of a Sector
20 Questions Chapter 10 Review. 1. Polygons The sum of the measures of the interior angles of a convex polygon is How many sides does the polygon.
Tangents to Circles (with Circle Review)
What Is There To Know About A Circle? Jaime Lewis Chrystal Sanchez Andrew Alas Presentation Theme By PresenterMedia.comPresenterMedia.com.
Areas of Circles, Sectors and Segments Lesson 11.6
7.7: Areas of Circles and Sectors
Area of Circles and Sectors Lesson 7.4A M.3.G.1 Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a particular.
Inscribed Angles Section 10.5.
 Solve problems involving geometric probability.  Solve problems involving sectors and segments of circles.
Chapter 11 Length and Area
Answers to homework problems – page 8
Warm – up 2. Inscribed Angles Section 6.4 Standards MM2G3. Students will understand the properties of circles. b. Understand and use properties of central,
10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.
Introduction Circles have several special properties, conjectures, postulates, and theorems associated with them. This lesson focuses on the relationship.
Warm Up Week 1. Section 10.3 Day 1 I will use inscribed angles to solve problems. Inscribed Angles An angle whose vertex is on a circle and whose.
Geometric Probability Sector – A region of a circle bounded by an arc of the circle and the two radii to the arc’s endpoints. Two important quantities.
105  32   16  36.5  105  Warm-up Find the measures of angles 1 – 4.
11.5 Geometric Probability
Circle GEOMETRY Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA.
Geometric Probability 5.8. Calculate geometric probabilities. Use geometric probability to predict results in real-world situations.
Chapter Circle  A set of all points equidistant from the center.
Area Area Probability Segment Probability Area of Segment Area of Sector Area of Circle.
4.5: Geometric Probability p M(DSP)–10–5 Solves problems involving experimental or theoretical probability. GSE’s Primary Secondary GSE’s M(G&M)–10–2.
Geometry Geometric Probability. October 25, 2015 Goals  Know what probability is.  Use areas of geometric figures to determine probabilities.
Geometry Review AREA 1. Find the measure of each interior angle of the regular polygon shown below. 2.
Chapter 11 Area of Polygons and Circles. Chapter 11 Objectives Calculate the sum of the interior angles of any polygon Calculate the area of any regular.
11.5 Geometric Probability Austin Varghese and Lane Driskill.
Inscribed Angles. Inscribed Angles and Central Angles A Central angle has a vertex that lies in the center of a circle. A n inscribed angle has a vertex.
Ch 11.6 What is the area of a square with an apothem length of 14 in? Round to the nearest tenth if necessary. What is the area of a regular hexagon with.
Chapter 11.5 Notes: Areas of Circles and Sectors Goal: You will find the areas of circles and sectors.
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.
Lesson 5 Menu 1.Find the area of the figure. Round to the nearest tenth if necessary. 2.Find the area of the figure. Round to the nearest tenth if necessary.
Geometric Probability “chance” Written as a percent between 0% and 100% or a decimal between 0 and 1. Area of “shaded” region Area of entire region Geometric.
Objectives: 1)To find the areas of circles, sectors, and segments of circles.
Objective After studying this section, you will be able to begin solving problems involving circles 9.2 Introduction to Circles.
Radian Measure Advanced Geometry Circles Lesson 4.
GEOMETRY HELP The length of the segment between 2 and 10 is 10 – 2 = 8. The length of the ruler is 12. P(landing between 2 and 10) = =, or length of favorable.
Circles. Circle  Is the set of all points in a plane that are equal distance from the center. This circle is called Circle P. P.
Warm - up Find the area of each figure. 1.A square with sides 12 in. 2.An equilateral triangle with sides 5 cm in 2 2.  10.8 cm 2.
Geometric Probability Probability Recall that the probability of an event is the likelihood that the event will occur.
Geometric probability Objective: To use segment and area models to find the probability of events.
Geometry 7-8 Geometric Probability. Review Areas.
Copyright © Cengage Learning. All rights reserved. 12 Geometry.
CIRCLES RADIUS DIAMETER (CHORD) CIRCUMFERENCE ARC CHORD.
9.3 Circles Objective: Students identify parts of a circle and find central angle measures.
CHAPTER 10.4 INSCRIBED ANGLES AND TANGENTS. An inscribed angle has a vertex on a circle and sides that contain chords of the circle. An intercepted arc.
Area of Circles Chapter 7B.
Chapter 7 Lesson 8 Objective: To use segment and area models to find the probabilities of events.
Section 7.5 More Area Relationships in the Circle
Chord Central Angles Conjecture
Introduction Circles have several special properties, conjectures, postulates, and theorems associated with them. This lesson focuses on the relationship.
Section 11.6 Geometric Probability
Module 19: Lesson 1 Central Angles & Inscribed Angles
Section 7.6: Circles and Arcs
Presentation transcript:

Geometric Probability – Solve problems involving geometric probability – Solve problems involving sectors and segments of circles To win at darts, you must throw the darts into the part of the dartboard that earns the most points. Probability that involves a geometric area such as length or area is called geometric probability.

GEOMETRIC PROBABILITY Key Concept Probability and Area A B 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

Example 1 Probability with Area A square gameboard has blue and white stripes of equal width as shown. What is the chance that a dart thrown at the board will land on a white stripe?

Example 1 Probability with Area A square gameboard has blue and white stripes of equal width as shown. What is the chance that a dart thrown at the board will land on a white stripe? Extend the sides of each stripe. This separates the square into 36 small unit squares. The white stripes have an area of 15 square units. The total area is 36 square units. The probability of tossing a dart into the white stripes is or

SECTORS AND SEGMENTS OF CIRCLES A sector of a circle is a region of a circle bounded by a central angle and its intercepted arc. Central Angle Arc Sector

Key Concept Area of a Sector 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 =  r 2 N°N° r N 360

Example 2 Probability with Sectors ° ° ° ° ° ° a)Find the area of the blue sector. 12 b)Find the probability that a point chosen at random lies in the blue sector.

chord arc segment The region of a circle bounded by an arc and a chord is called a segment of a circle. To find the area of a segment, subtract the area of a triangle formed by the radii and the chord from the area of the sector containing the segment.

Example 3 Probability with Segments 14 A regular hexagon is inscribed into a circle with a diameter of 14. a)Find the area of the red segment. b)Find the probability that a point chosen at random lies in the red segment.