Chance of winning Unit 6 Probability. Multiplication Property of Counting  If one event can occur in m ways and another event can occur in n ways, then.

Slides:

Advertisements

Similar presentations

1 Counting Techniques: Possibility Trees, Multiplication Rule, Permutations.

Advertisements

UNIT 4: Applications of Probability UNIT QUESTION: How do you calculate the probability of an event? Today’s Question: What is a permutation or combination.

GPS Algebra Day 2 ( ) UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1, MM1D2, MM1D3 Today’s Question:

Warm-Up Problem Can you predict which offers more choices for license plates? Choice A: a plate with three different letters of the alphabet in any order.

Consider the possible arrangements of the letters a, b, and c. List the outcomes in the sample space. If the order is important, then each arrangement.

Chapter 12 Sec 1 The Counting Principle. 2 of 25 Algebra 2 Chapter 12 Sections 1 thru 3 Independent Events An outcome is the result of a single trial.

Counting Principles The Fundamental Counting Principle: If one event can occur m ways and another can occur n ways, then the number of ways the events.

12.1 & 12.2: The Fundamental Counting Principal, Permutations, & Combinations.

Counting principle and permutations

Permutations and Combinations

Counting Principles and Probability Digital Lesson.

7 th Grade Chapter 11 Displaying and Analyzing Data Chapter 12 Using Probability.

Counting and Probability Sets and Counting Permutations & Combinations Probability.

Math I UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1-3 Today’s Question: How can I find the different.

The Fundamental Counting Principal, Permutations, & Combinations.

WonLost 1234 Year Number of Games Warm-Up 1) In which year(s) did the team lose more games than they won? 2) In which year did the team play.

6.2 Find Probability Using Permutations. Vocabulary n factorial: product of integers from 1 to n, written as n! 0! = 1 Permutation: arrangement of objects.

Permutations Lesson 10 – 4. Vocabulary Permutation – an arrangement or listing of objects in which order is important. Example: the first three classes.

7 Further Topics in Algebra © 2008 Pearson Addison-Wesley. All rights reserved Sections 7.4–7.7.

Counting Principles. What you will learn: Solve simple counting problems Use the Fundamental Counting Principle to solve counting problems Use permutations.

1 Fundamental Counting Principle & Permutations. Outcome-the result of a single trial Sample Space- set of all possible outcomes in an experiment Event-

Permutations and Combinations

1/31/2007 Pre-Calculus Chapter 9 Review a n = a 1 + (n – 1)d a n = a 1 r (n – 1)

Sports Camp Morning Camp AerobicsRunningYogaSwimmingWeights Afternoon Camp HikingTennisVolleyballSoftball List all the possible choices available on your.

Methods of Counting Outcomes BUSA 2100, Section 4.1.

Section 10-3 Using Permutations and Combinations.

Section 4.3 Objectives Use a tree diagram and the Fundamental Counting Principle to find probabilities Determine the number of ways a group of objects.

Probability Chapter 3. § 3.4 Counting Principles.

Lesson Counting Techniques. Objectives Solve counting problems using the Multiplication Rule Solve counting problems using permutations Solve counting.

Statistics 1: Elementary Statistics Section 4-7. Probability Chapter 3 –Section 2: Fundamentals –Section 3: Addition Rule –Section 4: Multiplication Rule.

Section 10.1 Introduction to Probability. Probability Probability is the overall likelihood that an event can occur. A trial is a systematic opportunity.

Counting – Day 1 Section 4.7. Why Do We Need Counting Methods? When finding a basic probability, what are the two things we need to know? Number of different.

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY S TATISTICS Section 3-6 Counting.

3.4 Counting Principles I.The Fundamental Counting Principle: if one event can occur m ways and a second event can occur n ways, the number of ways the.

Let’s work on some definitions Experiment- is a situation involving chance that leads to results called outcomes. An outcome is the result of a single.

Warm Up CST Review. EXAMPLE 1 Use a tree diagram Snowboarding A sporting goods store offers 3 types of snowboards (all-mountain, freestyle, and carving)

Ch Counting Principles. Example 1  Eight pieces of paper are numbered from 1-8 and placed in a box. One piece of paper is drawn from the box, its.

Thinking Mathematically

ProbabilityProbability Counting Outcomes and Theoretical Probability.

Counting Principles Multiplication rule Permutations Combinations.

11.1A Fundamental Counting Principal and Factorial Notation 11.1A Fundamental Counting Principal If a task is made up of multiple operations (activities.

Section 6.2: Probability Models Ways to show a sample space of outcomes of multiple actions/tasks: (example: flipping a coin and rolling a 6 sided die)

MATH 2311 Section 2.1. Counting Techniques Combinatorics is the study of the number of ways a set of objects can be arranged, combined, or chosen; or.

2.1 Factorial Notation (Textbook Section 4.6). Warm – Up Question  How many four-digit numbers can be made using the numbers 1, 2, 3, & 4?  (all numbers.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 11 Counting Methods and Probability Theory.

WonLost 1234 Year Number of Games Warm-Up 1) In which year(s) did the team lose more games than they won? 2) In which year did the team play.

1 2.3 Counting Sample Points (6)(6)(6)= 216 Example: How many outcome sequences are possible when a die is rolled three times?

The Fundamental Counting Principle and Permutations 18.0 Students use fundamental counting principles to compute combinations and permutations Students.

EXAMPLE 1 Count permutations

Counting Principles Ex. Eight pieces of paper are numbered 1 to 8 and placed in a box. One piece of paper is drawn from the box, its number is written.

Counting, Permutations, & Combinations

MATH 2311 Section 2.1.

Counting, Permutations, & Combinations

Copyright © 2016, 2013, and 2010, Pearson Education, Inc.

Fundamental Counting Principle

Counting Methods and Probability Theory

Apply the Counting Principle and Permutations

Counting, Permutations, & Combinations

Section 3-4 Permutations

Counting Principle and Permutations

Chapter 0.4 Counting Techniques.

Probability Multiplication Principles of Counting

6.2 Find Probability Using Permutations

Counting, Permutations, & Combinations

Counting, Permutations, & Combinations

MATH 2311 Section 2.1.

Counting Methods and Probability Theory

Counting Principle.

MATH 2311 Section 2.1.

Presentation transcript:

Chance of winning Unit 6 Probability

Multiplication Property of Counting  If one event can occur in m ways and another event can occur in n ways, then the number of ways that both events can occur together is m·n. The principle can be extended to three or more events

Example 1  At a sporting good store, skateboards are available in 8 different deck designs. Each deck design is available with 4 different wheel assemblies. How many skateboard choices does the store offer?

Addition Counting Principle  If the possibilities being counted can be divided into groups with no possibilities in common, then the total number of possibilities is the sum of the numbers of possibilities in each group.

Example 2  Every purchase made on a company’s website is given a random generated confirmation code. The code consists of 4 symbols (letters and digits). How many codes can be generated if at least one letter is used in each.

Finding Probabilities Using Permutations 6.2 pg. 342

Vocabulary  Factorials- for any positive integer n, the product of the integers from 1 to n is called n factorial and is written n!. Except 0! Which is equal to 1.

Examples  1. 6! = = 720 Find:  2. 10!  3. 8!

Vocab.  Permutations- an arrangement of objects in which order is IMPORTANT. The number of permutations of n objects is given by

Permutations  The number of permutations of n objects taken r at a time, where r ≤ n, is given by:  Used for the arrangement of objects in a specific order.

Examples 4. There are 5 students in the front row. How many ways can I call on each of them to present one of 5 problems on the board? 1 st 2 nd 3 rd 4 th 5 th So, I have = 120 ways to call on them. 5 things taken 5 at a time… 5 P 5

Example 5. What if we were choosing 5 people from the entire class? 1 st 2 nd 3 rd 4 th 5 th So there are 17, 100, 720 ways to choose 5.

Example 6. A 3-digit number is formed by selecting from the digits 4, 5, 6, 7, 8, and 9. There is no repetition. How many numbers are formed?

Example 7. How many of the numbers from Example 6 will be greater than 800?

Example 8. How many 3 digit numbers can be formed using the digits 1, 2, 3, 4 and 5, if repetition is allowed?

Example 9. How many different 4 letter words can be formed from the word CALM? (Assume any combo of 4 is a real word) 10. How many different 4 letter words can be formed from the word LULL? (Assume any combo of 4 is a real word) What’s the difference in 9 and 10?

Permutations The number of permutations of n things, taken n at a time, with r of those things identical is: 11. How many different 4 letter words can be formed from the word BABY?

Homework Text book Pg even

Combinations Section 6.3

Definition  A Combination is a selection of objects in which order is NOT important. The number of combination of n objects taken r at a time, where

Example  How many combinations of 3 letters from a list of A, B, C, D are there?

Example  For your school pictures, you can choose 4 backgrounds from a list of 10. How many combinations of backdrops are possible?

Example  Five students from the 90 students in your class will be selected to answer a questionnaire about participating in school sports. How many groups of 5 students are possible?

Homework  Page 349  Numbers even