Chapter 9 Lesson 3 The Fundamental Counting principle Objective: Use multiplication to count outcomes.

Slides:

Advertisements

Similar presentations

10.1 – Counting by Systematic Listing One-Part Tasks The results for simple, one-part tasks can often be listed easily. Tossing a fair coin: Rolling a.

Advertisements

Over Lesson 13–7 1) What is the probability of getting a 7 while rolling two number cubes? 2) What is the probability of rolling an odd number when rolling.

Compound Events SWBAT use tree diagrams and tables to find possible outcomes; find the number of possible outcomes using the counting principle; find the.

Lesson 14-1 Counting Outcomes. 5-Minute Check on Chapter 2 Transparency 3-1 Click the mouse button or press the Space Bar to display the answers. 1.Evaluate.

How many possible outcomes can you make with the accessories?

Permutations and Combinations AII Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish.

Expected value a weighted average of all possible values where the weights are the probabilities of each outcome :

Bell Work Three-course dinners can be made from the menu shown. Find the sample space for a dinner consisting of an appetizer, entrée, and dessert. Hint:

Counting Principal Warm-up (IN) Learning Objective: To use the counting principal to determine numbers of arrangements. You draw a card from a standard.

11-5 6th grade math Counting Methods.

13-1 Representing Sample Spaces You calculated experimental probability. Use lists, tables, and tree diagrams to represent sample spaces. Use the Fundamental.

40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Probability Lesson: PR-4 Fundamental Counting Principle Fundamental Counting Principle Learning.

The Counting Principle Counting Outcomes Have you ever seen or heard the Subway or Starbucks advertising campaigns where they talk about the 10,000 different.

Counting Principles Counting Principles Chapter 6.7.

Counting Methods Topic 1: Introduction to the Fundamental Counting Principle.

Section 10.1 A Counting Principle The Counting Principle andFactorials.

Chapter 12 – Probability and Statistics 12.1 – The Counting Principle.

Lesson 12-6 Pages Counting Outcomes. What you will learn! 1. How to use tree diagrams or the Fundamental Counting Principle to count outcomes.

Vocabulary Tree Diagram – A way for counting possible outcomes Sample Space – List of all possible outcomes Event – Any collection of one or more outcomes.

The Fundamental Counting Principle states that if there are x ways to choose a first item and y ways to choose a second item, then there are x(y) ways.

Transparency 2 Click the mouse button or press the Space Bar to display the answers.

March 10,  Counting  Fundamental Counting principle  Factorials  Permutations and combinations  Probability  Complementary events  Compound.

9-3 The Fundamental Counting Principle Pages Indicator(s)  D7.

Lesson 8.6 Page #1-21 (ODD), (EOO), (ODD), (EOO), (ODD) Pick up the handout on the table.

Lesson 9-3 Pages The Fundamental Counting Principle Lesson Check 9-2.

Transparency 3 Click the mouse button or press the Space Bar to display the answers.

Lesson 1 Menu Five-Minute Check (over Chapter 7) Main Idea and Vocabulary Targeted TEKS Example 1: Use a Tree Diagram Key Concept: Fundamental Counting.

Honors PreCalculus: Section 9.1 Basic Combinatorics.

Counting Principle 1.Suppose you have three shirts (red, black, and yellow) and two pair of pants (jeans and khakis). Make a tree diagram to find the number.

Lesson 0.4 (Counting Techniques)

6.7 Permutations and Combinations. Fundamental Counting You have the following clothes to choose from: 1 black and1 blue pair of jeans 1 yellow, 1 green,

37. Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

Counting Techniques. Multiplication Principle (also called the Fundamental Counting Principle) Combinations Permutations Number of subsets of a given.

 Counting  Fundamental Counting principle  Factorials  Permutations and combinations  Probability  Complementary events  Compound events  Independent.

Monday, March 31, 2014 AIM: What is the Multiplication Counting Principle?  DO NOW: Kimberly has three pair of pants: one black, one red, and one tan.

Counting Outcomes Objectives: (1) To develop fluency with counting strategies to determine the sample space for an event. Essential Questions: (1) How.

Combinations of Outcomes How Many Possible Outcomes Are There???

Chapter 3 Probability Initial Objective: Develop procedures to determine the # of elements in a set without resorting to listing them first. 3-6 Counting.

Chapter 12: Data Analysis & Probability 12.4 Counting Outcomes & Theoretical Probability.

Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

Permutations and Combinations

Permutations and Combinations

12-6 Counting Principle and Permutations

Topic: Probability Aim: How do we find the probability of compound events? Do Now: Three-course dinners can be made from the menu shown. (a) Find the sample.

Counting Outcomes.

Counting Principles and Tree Diagrams

Chapter 11 L11-2 Notes: Outcomes.

Lesson 11-1 Permutations and Combinations

Permutations and Combinations

Counting Outcomes.

How many possible outcomes can you make with the accessories?

12-6 Counting Principle and Permutations

Drill #83 Open books to page 645. Answer questions #1 – 4 .

Counting Principle.

Warm-Up Take out your Unit 1 pretest and complete question #2

Counting Outcomes.

Counting Outcomes.

Counting Outcomes.

Bellwork Practice Packet 10.3 B side #3.

Counting Outcomes.

Chances, Probabilities, and Odds

Permutations and Combinations

Permutations and Combinations

Lecture 7: Permutations and Combinations

Counting Methods and Probability Theory

Counting Methods and Probability Theory

Do Now Check Homework A B C D.

Presentation transcript:

Chapter 9 Lesson 3 The Fundamental Counting principle Objective: Use multiplication to count outcomes

The jean factory sells juniors’ jeans in different sizes and lengths. The table shows what is available. Sizeslength 3 Petite 5 Regular 7 Tall According to the table, how many sizes of juniors are there? 2.How many lengths are there? 3.Find the product of the two numbers you found in numbers 1 and 2. 4.Draw a tree diagram to find the number of different size and length combinations?

Fundamental Counting Principle Uses multiplication of the number of ways each event in an experiment can occur to find the number of possible outcomes in a sample space. Instead of using a tree diagram – just finds the number of outcomes

A famous steak house allows customers to create their own steak dinners. The choices are shown. How many different steak dinners are possible? SteakHow steaksPotatoes are cooked NY strip Raremashed Ribeye mediumbaked Filet welltwice baked PorterhouseAu gratin T-Bone 5x3x 4= 60 Types of # of ways types total number Steakto cookof potatoesof steak dinners

Example 3-1a CLOTHING The table below shows the shirts, shorts, and shoes in Gerry’s wardrobe. How many possible outfits can he choose consisting of one shirt, one pair of shorts, and one pair of shoes?ShirtsShortsShoesredbeigeblack bluegreenbrown whiteblue yellow

Example 3-1b number of shirts number of shorts number of shoes total number of outfits Check You can check your work by drawing a tree diagram and listing the 24 outcomes. Answer: There are 24 possible outfits that Gerry can choose.

Example 3-1c SANDWICHES The table below shows the types of bread, types of cheese, and types of meat that are available to make a sandwich. How many possible sandwiches can be made by selecting one type of bread, one type of cheese, and one type of meat?BreadCheeseMeatWhiteWheatRyeAmericanSwissMozzarellaTurkeyHam Roast Beef Answer: 27

Example 3-2a MULTIPLE-CHOICE TEST ITEM An orchestra has one opening for a violinist, one opening for a cellist, and one opening for an oboist. Three musicians are trying out for violin, five for cello, and three for oboe. Find the number of ways the openings can be filled. A 9 B 11 C 15 D 45 Read the Test Item To find the number of ways the openings can be filled, multiply the number of musicians trying out for violin, cello, and oboe.

Example 3-2b There are 3 musicians trying out for violin, 5 for cello, and 3 for oboe. So, there are or 45 ways the openings can be filled. Answer: D Solve the Test Item

Example 3-2c MULTIPLE-CHOICE TEST ITEM The school student council is electing one president, one secretary, and one treasurer. There are four students running for president, three running for secretary, and five running for treasurer. Find the number of ways the positions can be filled. A 12 B 60 C 15 D 45 Answer: B

Class work Complete numbers 9 – 15 on page 380

Homework Page 380 numbers 10 – 16 even