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Warm Up Write each fraction in simplest form. 1. 15 21 2. 48 64 3. 9 81 4. 30

Warm Up Write each fraction in simplest form. 1. 15 21 2. 48 64 3. 9 81 4. 30 45. 5 7. 3 4. 1 9. 2 3. Problem of the Day You roll a regular pair of number cubes. How likely is it that the product of the two numbers is odd and greater than 25? Explain.

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Warm Up Write each fraction in simplest form. 1. 15 21 2. 48 64 3. 9 81 4. 30

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  1. Warm Up Write each fraction in simplest form. 1.15 21 2.48 64 3. 9 81 4.30 45 5 7 3 4 1 9 2 3

  2. Problem of the Day You roll a regular pair of number cubes. How likely is it that the product of the two numbers is odd and greater than 25? Explain. Impossible; the only possible products greater than 25 (30 and 36) are even.

  3. Learn to use informal measures of probability.

  4. Vocabulary experiment complement trial outcome event probability simple event compound event

  5. An activity involving chance, such as rolling a cube, is called an experiment. Each repetition or observation of an experiment is a trial, and each result is an outcome. A set of one or more outcomes is an event. For example, rolling a 5 (one outcome) can be an event, or rolling an even number (more than one outcome) can be an event.

  6. The probabilityof an event, written P(event),is the measure of how likely an event is to occur. A simple event has a single outcome. A compound event is two or more simple events. Probability is a measure between 0 and 1, as shown on the number line. You can write probability as a fraction, a decimal, or a percent.

  7. Odd Not Odd 1, 3, 5 2, 4, 6 Additional Example 1A: Determining the Likelihood of an Event Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. rolling an odd number on a number cube There are 6 possible outcomes: Half of the outcomes are odd. Rolling an odd number is as likely as not.

  8. Less than 2 2 or more 1 2, 3, 4, 5, 6 Additional Example 1B: Determining the Likelihood of an Event Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. rolling a number less than 2 on a number cube There are 6 possible outcomes: Only one outcome is less than 2. Rolling a number less than 2 is unlikely.

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  10. When a number cube is rolled, either a 5 will be rolled or it will not. Rolling a 5 and not rolling a 5 are examples of complementary events. The complementof an event is the set of all outcomes that are not the event. Because it is certain that either an event or its complement will occur when an activity is performed, the sum of the probabilities is 1. P(event) + P(complement) = 1

  11. Additional Example 2: Using Complements A bag contains circular chips that are the same size and weight. There are 8 purple, 4 pink, 8 white, and 2 blue chips in the bag. The probability of drawing a pink chip is . What is the probability of not drawing a pink chip? 2 11 P(event) + P(complement) = 1

  12. 2 11 2 11 + P(not pink) = 1 Substitute for P(pink). 2 11 2 11 2 11 - = - Subtract from both t sides. 9 11 Simplify P(not pink) = 9 11 The probability of not drawing a pink chip is . Additional Example 2 Continued P(event) + P(complement) = 1 P(pink) + P(not pink) = 1

  13. http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=8094/8094.xmlhttp://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=8094/8094.xml

  14. Additional Example 3: School Application Mandy’s science teacher almost always introduces a new chapter by conducting an experiment. Mandy’s class finished a chapter on Friday. Should Mandy expect the teacher to conduct an experiment next week? Explain. Since the class just finished a chapter, they will be starting a new chapter. It is likely the teacher will conduct an experiment.

  15. http://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6917/6917.xmlhttp://my.hrw.com/math06_07/nsmedia/lesson_videos/msm2/player.html?contentSrc=6917/6917.xml

  16. Lesson Quiz for Student Response Systems 1. Determine whether the event is impossible, unlikely, likely, or certain. rolling a 7 on a number cube A. impossible B. unlikely C. likely D. certain

  17. Lesson Quiz for Student Response Systems 2. Determine whether the event is unlikely, as likely as not, likely, or certain. randomly drawing a black or white marble from a bag of black and white marbles A. impossible B. unlikely C. likely D. certain

  18. Lesson Quiz for Student Response Systems 3. Erika almost always goes out with an umbrella if it is a rainy day. Today is a rainy day. How likely is it that Erika will go out with umbrella today? A. impossible B. unlikely C. likely D. certain

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