Chapter 7 Lesson 8

1. Chapter 7 Lesson 8 Objective: To use segment and area models to find the probabilities of events.

2. 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

3. 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) = = = 7-3=4

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

5. 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%.

6. If the points of a region represent equally-likely outcomes, then you can find probabilities by comparing areas.

7. 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.

8. Assignment