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

3. Tree Diagrams: 1)Tossing Two Coins: Tails Heads Tails Coin 2Coin 1 Heads Tails Total Outcomes: _____ 4

4. 2)Tossing Three Coins: Total Outcomes: _____ TailsHeads_____ Tails_____ Coin 3 Coin 2 Coin 1 Heads _____ Tails_____ H H T T T T H H 8

5. 3)Tossing One Coin and One Number Cube: Number Cube Coin ____ Total Outcomes: _____ ____ H T 1 2 3 4 5 6 1 2 3 4 5 6 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 Do we have to use a tree diagram? Is there a shortcut?? Your turn to make a tree diagram...

7. 1)Tossing two coins: 2)Tossing three coins: 3) Tossing one coin and one number cube: 4) Spinning a spinner with eight equal regions, flipping two coins, and tossing one number cube: 4 8 12 192 Multiply the outcomes for EACH event...

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: 6)The total unique locker combinations for a four-digit locker code (using the digits 0 – 9): 7)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... Fundamental counting principle in action... How?? Think about it. The # of bread choices, times the # of meat choices, times the # of topping choices, times the # of sauce choices, etc., etc. It adds up fast!

10. TRIAL #1: Rolling Two Number Cubes Out of 20 trials, how many times will doubles occur– P(doubles)? 1) What do we need to know? # of doubles:____ total # of outcomes: ___ 2) Theoretical Probability: 3)Do the experiment (20 trials): 4) Experimental Probability: (what should happen) (what actually happens) 6 36

11. TRIAL #2 : Rolling a Number Cube and Flipping a Coin Out of 20 trials, how many times will heads and a # less than 3 occur– P(heads and a # < 3)? 1)What do we need to know? favorable outcomes: _____ total outcomes: _____ 2) Theoretical Probability: 3)Do the experiment (20 trials): 4) Experimental Probability: (what should happen) (what actually happens) 2 12

12. 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) ? P(1 st Event ) x P(2 nd Event) x =

13. 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”) 4)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)

14. 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.

15. 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: 1)Tossing Two Coins: 2)Tossing Three Coins: Compound Probability involves MORE than one event! Math-7 NOTES DATE: ______/_______/_______ 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. 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. NAME: TailsHeads_____ Tails_____ Coin 3 Coin 2 Coin 1 Heads _____ Tails_____ TailsHeadsTails Coin 2Coin 1 Heads Tails Total Outcomes: _____

16. 3)Tossing One Coin and One Number Cube: Is there a shortcut? 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 Number Cube Coin ____ Total Outcomes: _____

19. DATE: ______/_______/_______NAME:_____________________________________________________________________________

20. Coin 4 Coin 3 Coin 2 Coin 1 Child 1 Child 2 Child 3 Child 4

21. DATE: ______/_______/_______NAME:_____________________________________________________________________________