1. 10.6 Geometric Probability Alphabet Soup Mackenzie Mitchell – Elizabeth Mullins – Jacob Woodford

2. Vocabulary & Objectives VOCAB Geometric probability: a method of calculating probability based on a geometric measure such as length, angle measures or area Used when an experiment has an infinite number of outcomes ------------------------------------------------------------------------------ OBJECTIVES Calculate geometric probabilities Use geometric probabilities to predict results in real- world situations

3. Example #1- length related What is the probability that a random point on AB falls within one unit of point C? If the point falls between 1 unit to the right of C or 1 unit to the left of point C, that would be a suitable answer. AB C AB = 12 units AC = 2 units

4. Example #1- length related Our probability would be: 1 (  ) + 1 (  ) = 2 units Now divide this by the total possible places of selection (12) 2/12 = 1/6 There is one in six chance of having a random point fall within one unit of point C

5. Example #2- Angle Related: A If the red section is 80°, divide 80 by 360 (total number of °s) to find the probability of landing on that particular section.

6. Example #2: B To find the probability of landing on multiple sections, add up the angle measures of those sections and divide by 360.

7. Example #2: C To find the probability of not landing on one section, subtract that angle measure (example: yellow, 100°) from 360. Now take your new number (260) and divide it by 360 to find your probability. **Another way to do this is to add up the angle measures of every section except the specific one (example: yellow) and divide by 360.

8. Example #3- Using Area: A 1.Find the area of the shape (in this case: triangle) 1.Find the area of the rectangle 1.Divide the shape’s area by the rectangle’s area to find the probability 1.Ta- da!

9. Example #3: B 1.Find the area of the shape (in this case: trapezoid) 1.Find the area of the rectangle 1.Divide the shape’s area by the rectangle’s area to find the probability 1.Ta- da! Hello Einstein.

10. Example #3: C What is the probability that a random point in the blue rectangle will land in one of the three shapes? 1.Find the area of the shape (in this case: circle) 1.Find the area of the rectangle 1.Divide the shape’s area by the rectangle’s area to find the probability 1.Ta- da! You are a genius.

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