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Objectives: use segment and area models to find the probability of events

Section 7-8 Geometric Probability SPI 52A: determine the probability of an event. Objectives: use segment and area models to find the probability of events. Geometric Probability: Let points on a number line represent outcomes

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Objectives: use segment and area models to find the probability of events

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  1. Section 7-8 Geometric Probability SPI 52A: determine the probability of an event • Objectives: • use segment and area models to find the 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. Represent this using a segment. 3 4 P(waiting more than 15 minutes) = , or 45 60 Real-World: Finding Probability A museum offers a tour every hour. If Benny arrives at the tour site at a random time, what is the probability that he will have to wait at least 15 minutes? Because the favorable time is given in minutes, write 1 hour as 60 minutes. Benny may have to wait anywhere between 0 minutes and 60 minutes. Starting at 60 minutes, go back 15 minutes. The segment of length 45 represents Benny’s waiting more than 15 minutes. 3 4 The probability that Benny will have to wait at least 15 minutes is , or 75%.

  4. 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

  5. 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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