Name:Date:_/_/ Theoretical or Experimental Probability? Are the following situations examples of theoretical or experimental probability? 1. Finding the probability that Jeffrey will get an odd number with one roll of the number cube. A. Theoretical B. Experimental 2. At softball practice, Sarah hits 9 out of 13 balls pitched. Based on her rate, finding the probability that she will hit the next ball pitched. A. Theoretical B. Experimental Short Answer: 3. There are 8 red skittles, 2 yellow skittles, 4 green skittles, and 6 orange skittles in a bag. What is the probability of randomly selecting a green skittle P(green)? 4. Marissa has attempted 35 free throws. Of those attempted, 15 have gone in the basket. What is the experimental probability that Marissa s next free throw attempt will go in the basket? 5. The spinner shown was spun 20 times. Out of 20 spins, it landed on yellow 4 times. Compare the experimental probability with the theoretical probability. Experimental probability: Theoretical probability: Compare the results here:
Today s Lesson: What: Why: probability of compound events 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 one event. Tree Diagram shows the total possible outcomes of an event. Fundamental Counting Principle uses to determine the total possible outcomes when more than one event is combined. multiplication Calculating Compound Probability may use a tree diagram OR may _ MULTIPLY the first event TIMES the second event.
Tree Diagrams: 1) Tossing Two Coins: Coin 1 Coin 2 Total Outcomes: _ 4
2) Tossing Three Coins: Coin 1 Coin 2 Coin 3 H T H _ T _ H T H T Total Outcomes: _ 8
3) Tossing One Coin and One Number Cube: H Coin Number Cube 1 2 3 4 5 6 T 1 2 3 4 5 6 Total Outcomes: _ 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 Your turn to make a tree diagram... Do we have to use a tree diagram? Is there a shortcut?? Total Outcomes: _ 12
We can multiply to determine the outcomes... 1) Tossing two coins: Multiply the outcomes for EACH event... 4 2) Tossing three coins: 8 3) Tossing one coin and one number cube: 12 4) Spinning a spinner with eight equal regions, flipping two coins, and tossing one number cube: 192
36 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: 1,296 6) The total unique locker combinations for a four-digit locker code (using the digits 0 9): 10,000 7) Choosing from 12 types of entrees, 6 types of side dishes, 8 types of beverages, and 5 types of desserts: 2,880 8) Rolling two number cubes:
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!
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? 6 # of doubles: total # of outcomes: 2) Theoretical Probability: (what should happen) 36 6 36 or 1 6 3) Do the experiment (20 trials): 4) Experimental Probability: (what actually happens)
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: _ 12 total outcomes: _ 2 2) Theoretical Probability: (what should happen) 2 12 or 1 6 3) Do the experiment (20 trials): 4) Experimental Probability: (what actually happens)
1) 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: 1 2 x 1 2 = 1 4 P(1 st Event ) x P(2 nd 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 6 x 1 5 = 3 30 or 1 10
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 ) 4 143 1 11 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) 2 25 16 225 8 225
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 this slideshow (entitled Practice Work ) represent the homework assigned for this lesson.
NAME: What: Math-7 NOTES probability of compound events DATE: / / 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: 1) Tossing Two Coins: Coin 1 Coin 2 Total Outcomes: _ 2) Tossing Three Coins: Coin 1 Coin 2 Coin 3 Total Outcomes: _
3) Tossing One Coin and One Number Cube: Coin 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 Is there a shortcut? Total Outcomes: _
We can multiply to determine the outcomes...
NAME:_ DATE: / / probability of compound events
NAME:_ DATE: / / probability of compound events 1 6 x 1 6 = 1 36 1 9 x 1 5 = 1 45
Draw a tree diagram for the questions below. Use the results to answer each question. #1 Find the probability of getting exactly three tails when four coins are tossed. Coin 1 Coin 2 Coin 3 Coin 4 #2 Find the probability that a family with four children has exactly four girls. Child 1 Child 2 Child 3 Child 4 #3 In problem 2, what is the probability that the family has two boys and two girls in any order?