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Today’s Lesson:

Today’s Lesson:. What : probability of compound events Why: To create and analyze tree diagrams; discover and use the fundamental counting principle; and use multiplication to calculate compound probability. Compound Probability involves MORE than one event!. Vocabulary:

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Today’s Lesson:

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  1. Today’s Lesson: What: probability of compound events Why: To create and analyze tree diagrams; discover and use the fundamental counting principle; and use multiplication to calculate compound probability.

  2. Compound Probability involves MORE than one event! Vocabulary: Compound Probability- refers to probability of more than ____________ event. Tree Diagram– shows the total possible __________________ of an event. Fundamental Counting Principle– used to determine the total possible ____________________ when more than one event is combined. Calculating Compound Probability– may use a tree diagram OR may _________________ the first event TIMES the second event. one outcomes outcomes MULTIPLY

  3. Tree Diagrams: Tossing Two Coins: Total Outcomes: _____ 4

  4. Tossing Three Coins: H T H T H T H T Total Outcomes: _____ 8

  5. 3) Tossing One Coin and One Number Cube: 1 2 3 H 4 5 6 1 2 3 T 4 5 6 Total Outcomes: _____ 12

  6. 4) Choosing a Sundae with the following choices (may only choose one from each category): Chocolate or Vanilla Ice cream Fudge or Caramel Sauce Sprinkles, Nuts, or Cherry Total Outcomes: _____ 12

  7. Fundamental counting principle How many outcomes?? Tossing two coins: Tossing three coins: 4 8 3) Tossing one coin and one number cube: Spinning a spinner with eight equal regions, flipping two coins, and tossing one number cube: 12 192

  8. 5) The total unique four-letter codes that can be created with the following letter choices (each letter can be used more than once)-- A, B, C, D, E, and F: The total unique locker combinations for a four-digit locker code (using the digits 0 – 9): Choosing from 12 types of entrees, 6 types of side dishes, 8 types of beverages, and 5 types of desserts: 8) Rolling two number cubes: 1,296 10,000 2,880 36

  9. 36,864 ways to “dress” a whataburger . . .

  10. Rolling two number cubes How many outcomes?? A. Fill-in-the-chart: 5 6 7 8 9 10 6 7 8 6 9 10 7 11 8 7 4 8 5 9 6 10 7 8 11 12 9 36 6 0 1 5 2 4 3 3 2 4 5 1 Using the dice diagram from Part A above, what is the probability of rolling doubles?

  11. PROBABILITY TRIALS 6 (what should happen) 36 (what actually happens)

  12. PROBABILITY TRIALS 2 (what should happen) 12 (what actually happens)

  13. Compound Probability sample questions: When two coins are tossed, what is the probability of both coins landing on heads – P (H and H) ? We can draw a tree diagram to answer this. OR, we can use MULTIPLICATION to solve: x = P(1st Event ) x P(2nd Event) 2) When a number cube is rolled and the spinner shown is spun, what is the probability of landing on an even # and orange– P(even # and orange) ? x =

  14. A card is drawn from a standard deck of cards and a letter is picked from a bag containing the letters M-A-T-H-E-M-A-T-I-C-S: a) P(ace and a vowel) b) P(red card and a “T”) A bag contains 3 grape, 4 orange, 6 cherry, and 2 chocolate tootsie pops. Once a pop is picked, it is placed back into the bag: a) P(grape , then cherry) b) P(two oranges in a row) c) P(chocolate , then orange)

  15. END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

  16. NAME: DATE: ______/_______/_______ Math-7 NOTES What: probability of compound events Why: To create and analyze tree diagrams; discover and use the fundamental counting principle; and use multiplication to calculate compound probability. Compound Probability involves MORE than one event! Vocabulary: Compound Probability- refers to probability of more than _______________ event. Tree Diagram– shows the total possible _______________________ of an event. Fundamental Counting Principle– used to determine the total possible outcomes when ________________than one event is combined. Calculating Compound Probability– may use a tree diagram OR may _________________ the first event TIMES the second event. Tree Diagrams: Tossing Two Coins: Tossing Three Coins: Total Outcomes: _____ Total Outcomes: _____

  17. 3) Tossing One Coin and One Number Cube: Total Outcomes: _____ 4) Choosing a Sundae with the following choices (may only choose one from each category): Chocolate or Vanilla Ice cream Fudge or Caramel Sauce Sprinkles, Nuts, or Cherry Total Outcomes: _____ Is there a shortcut?

  18. Fundamental counting principle How many outcomes?? Tossing two coins: Tossing three coins: The total unique four-letter codes that can be created with the following letter choices (each letter can be used more than once)-- A, B, C, D, E, and F: The total unique locker combinations for a four-digit locker code (using the digits 0 – 9): Choosing from 12 types of entrees, 6 types of side dishes, 8 types of beverages, and 5 types of desserts: Rolling two number cubes: 3) Tossing one coin and one number cube: Spinning a spinner with eight equal regions, flipping two coins, and tossing one number cube:

  19. Rolling two number cubes How many outcomes?? A. Fill-in-the-chart: Using the dice diagram from Part A above, what is the probability of rolling doubles?

  20. PROBABILITY TRIALS (what should happen) (what actually happened) (what should happen) (what actually happened)

  21. Compound Probability sample questions: When two coins are tossed, what is the probability of both coins landing on heads – P (H and H)? We can draw a tree diagram to answer this. OR, we can use MULTIPLICATION to solve: x = P(1st Event ) x P(2nd Event) 2) When a number cube is rolled and the spinner shown is spun, what is the probability of landing on an even # and orange– P(even # and orange) ? 3) A card is drawn from a standard deck of cards and a letter is picked from a bag containing the letters M-A-T-H-E-M-A-T-I-C-S: a) P(ace and a vowel) b) P(red card and a “T”) A bag contains 3 grape, 4 orange, 6 cherry, and 2 chocolate tootsie pops. Once a pop is picked, it is placed back into the bag: a) P(grape , then cherry) b) P(two oranges in a row) c) P(chocolate , then orange)

  22. NAME:_____________________________________________________________________________NAME:_____________________________________________________________________________ DATE: ______/_______/_______ Math-7 practice/homework “probability of compound events”

  23. NAME:_____________________________________________________________________________NAME:_____________________________________________________________________________ DATE: ______/_______/_______ Math-7 practice/ Homework “probability of compound events” x = x =

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