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

## Presentation on theme: "Today’s Lesson: What: probability of compound events Why: To create and analyze tree diagrams; discover and use the fundamental counting principle; and."— Presentation transcript:

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.

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. Compound Probability involves MORE than one event! one outcomes MULTIPLY

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

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

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

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

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

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

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

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

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

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 =

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)

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.

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: _____

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: _____

1)Tossing two coins: 2)Tossing three coins: 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: 3) Tossing one coin and one number cube: 4)Spinning a spinner with eight equal regions, flipping two coins, and tossing one number cube:

C.Using the dice diagram from Part A above, what is the probability of rolling doubles? A. Fill-in-the-chart:

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 happened) 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 happened)

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”) 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) P(1 st Event ) x P(2 nd Event)

DATE: ______/_______/_______NAME:_____________________________________________________________________________

Coin 4 Coin 3 Coin 2 Coin 1

DATE: ______/_______/_______NAME:_____________________________________________________________________________

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