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Section 10-8 Geometric Probability

Section 10-8 Geometric Probability. Objectives: use segment and area models to calculate the geometric probability of events. Geometric Probability: Let points on a number line represent outcomes Find probability by comparing measurements of sets of points

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Section 10-8 Geometric Probability

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  1. Section 10-8 Geometric Probability • Objectives: • use segment and area models to calculate the geometric probability of events • Geometric Probability: • Let points on a number line represent outcomes • Find probability by comparing measurements of sets of points • P(event) = length of favorable segment • length of entire segment

  2. length of favorable segment length of entire segment 8 12 Finding Probability using Segments A gnat lands at random on the edge of the ruler below. Find the probability that the gnat lands on a point between 2 and 10. 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) = 2 3 = =

  3. Find the area of the circle. Because the square has sides of length 20 cm, the circle’s diameter is 20 cm, so its radius is 10 cm. A = r 2 = (10)2 = 100 cm2 Find the area of the region between the square and the circle. A = (400 – 100 ) cm2 Finding Probability using Area A circle is inscribed in a square target with 20-cm sides. Find the probability that a dart landing randomly within the square does not land within the circle. 20 cm Find the area of the square. A = s2 = 202 = 400 cm2 ..continued

  4. area between square and circle area of square 400 – 100 400 Use areas to calculate the probability that a dart landing randomly in the square does not land within the circle. Use a calculator. Round to the nearest thousandth. P (between square and circle) = = 0.2146 The probability that a dart landing randomly in the square does not land within the circle is about 21.5%.

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