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Counting Methods

Counting Methods. Lesson 11-5 Pg. # 426-428. CA Content Standards. Statistics, Data Analysis, and Probability 3.1 ***: I represent all possible outcomes of compound events in an organized way and express the theoretical probability of each outcome.

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Counting Methods

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  1. Counting Methods Lesson 11-5 Pg. # 426-428

  2. CA Content Standards • Statistics, Data Analysis, and Probability 3.1 ***: I represent all possible outcomes of compound events in an organized way and express the theoretical probability of each outcome. • Statistics, Data Analysis, and Probability 3.3***: I represent probabilities as ratios and percentages between 0 and 100.

  3. Vocabulary: TREE DIAGRAM • A diagram used to organize outcomes of an experiment to make them easier to count.

  4. Vocabulary: COUNTING PRINCIPLE • If one choice can be made in m ways and a second choice can be made in n ways, then the two choices can be made together in m x n ways.

  5. Objective • Use a tree diagram or the counting principle to find the total number of outcomes for an event. • Math Link: You can use what you know about making tables and tree diagrams to find all possible outcomes.

  6. Example 1. • The cooking club is having a sandwich fundraiser. A sandwich consists of one choice of bread and one choice of filling. How many different kinds of sandwiches can be made with the following ingredients? • Bread: Pita, Tortilla • Filling: Chicken, Beef, Vegetable

  7. You can use a tree diagram… • To represent the different kinds of sandwiches. Menu includes: pc, pb, pv, tc, tb, tv

  8. Example 2. • One of each type of sandwich is prepared. You choose one without looking. Find the probability of getting a beef sandwich. • The menu includes 6 kinds of sandwiches: pc, pb, pv, tc, tb, tv • 2 kinds of sandwiches have beef: pb, tb • So… P(beef) = 2/6 = 1/3 = 33% • The probability of getting a beef sandwich is about 33%.

  9. Example 3. • If there are three kinds of breads and four kinds of fillings at the fundraiser, how many different kinds of sandwiches can be made? • Use the counting principle. Possible Possible Kinds of Breads Fillings Sandwiches 3 x 4 = 12 • Twelve different kinds of sandwiches could be made. If there are m possible outcomes for the first event and n possible outcomes for the second event, then there are m x n possible outcomes.

  10. Moral of the Story • Use tree diagrams to organize possible outcomes. Also, if there are m possible outcomes for the first event and n possible outcomes for the second event, then there are m x n total possible outcomes.

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