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

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

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

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

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.

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

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.

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!

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.

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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