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

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) = length of favorable segment length of entire segment 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. Finding Probability using Segments ==

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. P(waiting more than 15 minutes) =, or Represent this using a segment. The probability that Benny will have to wait at least 15 minutes is, or 75% Real-World: Finding Probability

Find the area of the square. A = s 2 = 20 2 = 400 cm 2 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 cm 2 Find the area of the region between the square and the circle. A = (400 – 100 ) cm 2 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. Finding Probability using Area 20 cm

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. The probability that a dart landing randomly in the square does not land within the circle is about 21.5%. P (between square and circle) = = area between square and circle area of square 400 –