Chapter 7 Lesson 8

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Chapter 7 Lesson 8

• Objective To use segment and area models to find
  the probabilities of events.

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The probability of an event is the ratio of the
number of favorable outcomes to the number of
possible outcomes.
                                               
                                                  
          Sometimes you can use a Geometric
Probability model in which you let points
represent outcomes. You find probabilities by
comparing measurements of sets of points. For
example, if points of segments represent
outcomes, then                                 
                                                  
                                      
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Example 1 Finding Probability Using Segments
A fly lands at a random point on the ruler's
edge. Find the probability that the point is
between 3 and 7.                               
                                                  
                                                  
                                             
                      P(landing between 3 and 7)

7-34
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Example 2 Finding Probability Using Segments
A point on    is selected at random. What is
the probability that it is a point on    ?
                         
8-44
P(landing between 4 and 8)

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Example 3 Finding Probability Using Segments
Anna's bus runs every 25 minutes. If she arrives
at her bus stop at a random time, what is the
probability that she will have to wait at least
10 minutes for the bus? Assume that a stop
takes very little time, and let    represent
the 25 minutes between buses. If Anna arrives at
any time between A and C, she has to wait at
least 10 minutes until B. P(waiting at least
10 min)                           , or
    The probability that Anna will have to wait
at least 10 minutes for the bus is     or 60.
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If the points of a region represent
equally-likely outcomes, then you can find
probabilities by comparing areas.
                                                  
                                                  
        
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Example 4 Finding Probability Using Area
Assume that a dart you throw will land on the
1-ft square dartboard and is equally likely to
land at any point on the board. Find the
probability of hitting each of the blue, yellow,
and red regions. The radii of the concentric
circles are 1, 2, and 3 inches, respectively.
                                                 
                                                  
                                                  
                                                  
                                          
The probabilities of hitting the blue, yellow,
and red regions are about 2.2, 6.5, and 10.9,
respectively.
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Assignment
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