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Geometric Probability

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.)

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Geometric Probability

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  1. 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 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other attributes (Ex. How does changing the radius or height of a cylinder affect its surface area or volume?) R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles Geometric Probability

  2. Probability Review • Probability: The chance that a desired outcome will occur out of all possible outcomes

  3. Probability Review • A probability will always be a decimal between 0 and 1 • We express a probability as a percent

  4. Non-Geometric Example • Josh has 6 red skittles, 4 purple skittles, 3 green skittles, and 9 yellow skittles in a bag. If he draws one skittle at random, what is the probability that he will draw a green skittle?

  5. Geometric Probability • Geometric probability: Given a figure, the probability that a randomly chosen point would lie in the preferred region

  6. Example A dart is thrown at random at this dart board. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region. Note: on some problems the probability can just be reasoned! 4 6

  7. More Examples A dart is thrown at random at this dart board. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region.

  8. Example A dart is thrown at random at this dart board. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region. What do you notice about this? If dimensions aren’t given, CHOOSE YOUR OWN A good number to use is, An Even Number

  9. Example A dart is thrown at random at this dart board. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region. This is a square with semi-circles.

  10. 12’ 6’ Now You Try… A dart is thrown at random at this dart board. If the dart hits the board, find the probability to the nearest percent that it will land in the shaded region.

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