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Understanding Probability: Fractions, Products, and Likelihood

Explore probability concepts through fractions, products of dice rolls, and informal measures of likelihood. Learn vocabulary and practice classifying events as impossible, unlikely, likely, or certain.

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Understanding Probability: Fractions, Products, and Likelihood

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  1. Probability 10-1 Course 2 Warm Up Problem of the Day Lesson Presentation

  2. Probability 10-1 Course 2 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

  3. Probability 10-1 Course 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.

  4. Probability 10-1 Course 2 Learn to use informal measures of probability.

  5. Probability 10-1 Course 2 Insert Lesson Title Here Vocabulary experiment outcome event probability equally likely impossible certain

  6. Probability 10-1 Course 2 Suppose you rolled one of these dice. The blue one is equally likely to land on any of the six numbers. The red one is more likely to land on one of the larger faces. So the likelihood is greater that you would roll a 5 with the red die than with the blue one.

  7. Probability 10-1 Course 2 Any activity involving chance, such as the roll of a die, is an experiment. The result of an experiment is an outcome. An event is a set of one or more outcomes. Events that have the same probability are equally likely. Probabilityis the measure of how likely an event is to occur. The more likely an event is to occur, the higher its probability. The less likely an event is to occur, the lower its probability.

  8. Probability 10-1 Course 2 Additional Example 1A: Determining the Likelihood of an Event A bag contains circular chips that are the same size and weight. There are 8 purple chips, 4 pink chips, 8 white chips, and 2 blue chips in the bag. A.Would you be more likely to pull a purple chip or a blue chip from the bag? Since there are more purple chips than blue chips in the bag, it is more likely you would pull a purple chip than a blue chip from the bag.

  9. Probability 10-1 Course 2 Additional Example 1B: Determining the Likelihood of an Event A bag contains circular chips that are the same size and weight. There are 8 purple chips, 4 pink chips, 8 white chips, and 2 blue chips in the bag. B. Would you be more likely to pull a white chip or a purple chip from the bag? Since the number of white chips equals the number of purple chips in the bag, it is just as likely that you would pull a white chip as a purple from the bag. The events are equally likely.

  10. Probability 10-1 Course 2 Insert Lesson Title Here Try This: Example 1A A bag contains 16 marbles that are similar in weight and size. There are 8 blue marbles, 4 red marbles, 2 white marbles, and 2 yellow marbles in the bag. A. Would you be more likely to pull a white or a yellow marble from the bag? Since there are an equal number of white marbles and yellow marbles, it is just as likely that you would pull a white marble as a yellow marble. The events are equally likely.

  11. Probability 10-1 Course 2 Insert Lesson Title Here Try This: Example 1B A bag contains 16 marbles that are similar in weight and size. There are 8 blue marbles, 4 red marbles, 2 white marbles, and 2 yellow marbles in the bag. B. Would you be more likely to pull out a yellow marble or a red marble? Since there are more red marbles than yellow marbles, it is more likely that you would pull a red marble than a yellow marble.

  12. Probability 10-1 As likely as not Impossible Unlikely Likely Certain Course 2 Every event is either impossible, certain, or somewhere between these extremes. An event is mathematically impossible if it can never happen and mathematically certain if it will always happen. If an event is as likely as not, the probability that it will happen is the same as the probability that it will not happen.

  13. Probability 10-1 Course 2 Additional Example 2A: Classifying Likelihood Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. A. Tina has a soccer game on Saturday. How likely is it that she is at home all day on Saturday? Tina could have gotten sick on Saturday morning and stayed home. However, it is unlikely that she is at home on Saturday.

  14. Probability 10-1 Course 2 Additional Example 2B: Classifying Likelihood Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. B. Jason is canoeing on the river. How likely is it that he is shopping with Kevin? It is impossible that Jason is shopping with Kevin.

  15. Probability 10-1 Course 2 Additional Example 2C: Classifying Likelihood Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. C. Maureen is running with her mother. Her mother is in the park. How likely is it that Maureen is at the park? It is certain that Maureen is running at the park.

  16. Probability 10-1 Course 2 Additional Example 2D: Classifying Likelihood Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. D. There are 12 black and 12 red checkers in a box. How likely is it that you will randomly draw a red checker? Since the number of black checkers equals the number of red checkers, it is as likely as not that you will draw a red checker.

  17. Probability 10-1 Course 2 Insert Lesson Title Here Try This: Example 2A Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. A. The math class has a test each Friday. Today is Friday. How likely is it that the math class will be having a test today? It is certain that the math class will have a test today.

  18. Probability 10-1 Course 2 Insert Lesson Title Here Try This: Example 2B Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. B. Gerald has never played two tennis matches in one day. He already played one match today. How likely is it that he will play another match? Since Gerald has never played two tennis matches in one day, it is unlikely that he will play another match today.

  19. Probability 10-1 Course 2 Insert Lesson Title Here Try This: Example 2C Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. C. Maggie has a doctor’s appointment Monday morning. How likely is it she will miss some classes Monday morning? It is likely that Maggie will miss some classes Monday morning.

  20. Probability 10-1 Course 2 Insert Lesson Title Here Try This: Example 2D Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. D. There are five 2’s and five 3’s in a set of 10 cards. If you draw a card, how likely is it that you will randomly draw a 3? Since the number of 2’s equals the number of 3’s, it is as likely as not that you will draw a 3.

  21. Probability 10-1 Course 2 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.

  22. Probability 10-1 Course 2 Insert Lesson Title Here Try This: Example 3 After completing a unit chapter, Alice’s keyboarding class usually begins the next class day with a time trial exercise, practicing the previously learned skills. It is Wednesday and a unit chapter was completed the previous day. Will the class start with a time trial exercise? If the teacher keeps to her planned schedule, it is likely the class will start with a time trial.

  23. Probability 10-1 Course 2 Insert Lesson Title Here Lesson Quiz: Part 1 A bag holds 4 red marbles, 3 green marbles, 3 yellow marbles, and 2 blue marbles. You pull one out without looking. 1. Is it more likely to be red or blue? red 2. Is it more likely to be green or yellow? equally likely

  24. Probability 10-1 Course 2 Insert Lesson Title Here Lesson Quiz: Part 2 Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. 3. Bonnie’s Spanish club meets on Tuesday afternoons. How likely is it that Bonnie is at the mall on Tuesday afternoon? 4. There are 12 SUVs and 12 vans in a parking lot. How likely is it that the next vehicle to move is a van? unlikely as likely as not

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