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Sample Spaces and Counting Principles in Probability

Learn how to use lists, tree diagrams, and the Fundamental Counting Principle to find sample spaces and calculate probabilities. Practice with examples and exercises.

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Sample Spaces and Counting Principles in Probability

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 7–4) Main Idea and Vocabulary Example 1: Use a List to Find a Sample Space Example 2: Use a Tree Diagram to Find Sample Space Example 3: Use Fundamental Counting Principle Lesson Menu

  3. Construct sample spaces using tree diagrams or lists. • Fundamental Counting Principle • sample space • tree diagram Main Idea/Vocabulary

  4. Use a List to Find Sample Space VACATIONWhile on vacation, Carlos can go snorkeling, boating, and paragliding. In how many ways can Carlos do the three activities? Make an organized list to show the sample space. Make an organized list. Use S for snorkeling, B for boating, and P for paragliding. SBP SPB BSP BPS PSB PBS Answer: There are 6 ways Carlos can do the three activities. Example 1

  5. A B C D STUDENT COUNCIL Ken, Betsy, Sally, and David are seated in a row at the head table at a student council meeting. In how many ways can the four students be seated? A. 8 B. 12 C. 16 D. 24 Example 1

  6. Use a Tree Diagram to Find Sample Space A car can be purchased with either two doors or four doors. You may also choose leather, fabric, or vinyl seats. Use a tree diagram to find all the buying options. List each choice for the number of doors. Then pair each choice for the number of doors with each choice for the type of seats. Example 2

  7. Use a Tree Diagram to Find Sample Space Answer: There are six possible buying options. Example 2

  8. A B C D A pair of sneakers can be purchased with either laces or Velcro. You may also choose white, gray, or black sneakers. Use a tree diagram to find how many different sneakers are possible. A. 3 B. 5 C. 6 D. 8 Example 2

  9. Use Fundamental Counting Principle FLOWERS Chloe wants to buy a bouquet of flowers in a vase. The flower shop has roses, daffodils, and tulips and has four different vases from which to choose. Use the Fundamental Counting Principle to find the total number of possible outcomes of a bouquet made up of two types of flowers in a vase. number of outcomes for flower choice number of outcomes for vase choice total number of outcomes • = = 3 • 4 12 Example 3

  10. Use Fundamental Counting Principle Answer: There are 12 different outcomes. Example 3

  11. A B C D PASTA A restaurant offers a pasta bar where customers can choose from fettuccine, linguine, and macaroni for their pasta choice, and three types of sauce. Use the Fundamental Counting Principle to find the total number of outcomes of a pasta dish with one type of pasta and one sauce. A. 3 B. 6 C. 9 D. 12 Example 3

  12. End of the Lesson End of the Lesson

  13. Five-Minute Check (over Lesson 7–4) Image Bank Math Tools Animation Menu Probability and Area Resources

  14. 7-2Circle Graphs 7-8Estimating With Percents Animation Menu

  15. A B C D A.% B.% C. % D.% (over Lesson 7-4) A ten-sided number cube with the numbers 1–10 on it is rolled. Find the probability of the event P(3). Write the answer as a fraction, a decimal, and a percent. Five Minute Check 1

  16. A B C D A. % B. % C.% D.% (over Lesson 7-4) A ten-sided number cube with the numbers 1–10 on it is rolled. Find the probability of the event P(1 or 2). Write the answer as a fraction, a decimal, and a percent. Five Minute Check 2

  17. A B C D A.% B.% C. % D.% (over Lesson 7-4) A ten-sided number cube with the numbers 1–10 on it is rolled. Find the probability of the event P(4 or less). Write the answer as a fraction, a decimal, and a percent. Five Minute Check 3

  18. A B C D A. % B.% C. % D.% (over Lesson 7-4) A ten-sided number cube with the numbers 1–10 on it is rolled. Find the probability of the event P(not a multiple of 3). Write the answer as a fraction, a decimal, and a percent. Five Minute Check 4

  19. A B C D A.B. C.D. (over Lesson 7-4) A petting zoo has five goats, four camels, and a ferret. If the zookeeper knows that only one animal got out and all animals had an equal chance of getting out, what is the chance that it was the ferret? Write the answer as a fraction, a decimal, and a percent. Five Minute Check 5

  20. A B C D A. B. C. D. (over Lesson 7-4) What is the chance of drawing any king in a deck 52 cards? Five Minute Check 6

  21. End of Custom Shows

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