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

Slides:

Advertisements

Similar presentations

Probability Topic 5: Probabilities Using Counting Methods.

Advertisements

In this lesson we single out two important special cases of the Fundamental Counting Principle permutations and combinations. Goal: Identity when to use.

Permutations and Combinations

Chapter 8 Counting Principles: Further Probability Topics Section 8.3 Probability Applications of Counting Principles.

Thinking Mathematically

Math in Our World Section 11.2 Combinations.

Chapter 11 Counting Methods © 2008 Pearson Addison-Wesley. All rights reserved.

Probability Using Permutations and Combinations

Thinking Mathematically

If you have a small bag of skittles and you separate then, you have 5 blue, 6 red, 3 purple, and 5 yellow. What is the probability that you would pick.

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

Chapter Probability © 2010 Pearson Prentice Hall. All rights reserved 3 5.

Logic and Introduction to Sets Chapter 6 Dr.Hayk Melikyan/ Department of Mathematics and CS/ For more complicated problems, we will.

College Algebra Fifth Edition

Chapter 7 Logic, Sets, and Counting Section 4 Permutations and Combinations.

Probability Topic 5: Probabilities Using Counting Methods.

Chapter 12 Section 7 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Aim: Combinations Course: Math Lit. Do Now: Aim: How do we determine the number of outcomes when order is not an issue? Ann, Barbara, Carol, and Dave.

Chapter 12 Section 7 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Probability and Counting Rules CHAPTER 4.5.  Find the probability of getting four aces when five cards are drawn from an ordinary deck of cards. FOUR.

Chapter 11 Counting Methods © 2008 Pearson Addison-Wesley. All rights reserved.

1 Combinations. 2 Permutations-Recall from yesterday The number of possible arrangements (order matters) of a specific size from a group of objects is.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 12.3, Slide 1 12 Counting Just How Many Are There?

Permutation and Combination

Algebra 2 Thursday Today, we will be able to… Find the probability of two independent events Find the probability of two dependent events Find.

© The McGraw-Hill Companies, Inc., Chapter 4 Counting Techniques.

Notes Over 12.3 Finding Probabilities of Events

Prob/Stats Definition A permutation is an ordered arrangement of objects. (For example, consider the permutations of the letters A, B, C and D.)

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Chapter 7 Logic, Sets, and Counting Section 4 Permutations and Combinations.

Section 11.2 Combinations Math in Our World Learning Objectives  Distinguish between combinations and permutations.  Find the number of combinations.

Aim #10-7: How do we use the permutation formula? A permutation is an ordered arrangement of items that occurs when: No item is used more than once. The.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 12.3, Slide 1 12 Counting Just How Many Are There?

Chapter 11 Counting Methods © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter Probability © 2010 Pearson Prentice Hall. All rights reserved 3 5.

Probability and Counting Rules

Aim: Combinations Course: Alg. 2 & Trig. Do Now: Aim: How do we determine the number of outcomes when order is not an issue? Ann, Barbara, Carol, and.

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

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

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

Copyright © 2015, 2011, 2008 Pearson Education, Inc. Chapter 7, Unit B, Slide 1 Probability: Living With The Odds 7.

COUNTING Permutations and Combinations. 2Barnett/Ziegler/Byleen College Mathematics 12e Learning Objectives for Permutations and Combinations  The student.

MAT 142 Lecture Video Series. Combinatorics and Probability.

Counting Techniques (Dr. Monticino). Overview  Why counting?  Counting techniques  Multiplication principle  Permutation  Combination  Examples.

MATHPOWER TM 12, WESTERN EDITION Chapter 8 Probability

© 2010 Pearson Prentice Hall. All rights reserved. 1 §11.5, Probability with the Fundamental Counting Principle, Permutations, and Combinations.

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.

MAT 142 Lecture Video Series

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

Probability and Combinatorics

Counting Methods and Probability Theory

Chapter 10 Counting Methods.

4-6 Probability and Counting Rules

Unit 4 – Combinatorics and Probability Section 4

Chapter 0.4 Counting Techniques.

Do Now If fours cards are drawn from a deck without replacement, find the probability of getting these results: All kings All diamonds All sevens.

Lial/Hungerford/Holcomb: Mathematics with Applications 10e

4 Probability Lesson 4.8 Combinations and Probability.

Permutations and Combinations

Counting Methods and Probability Theory

Section Solving Probability Problems by Using Combinations

Chapter 10 Counting Methods 2012 Pearson Education, Inc.

Counting Methods and Probability Theory

Counting Methods and Probability Theory

Lial/Hungerford/Holcomb: Mathematics with Applications 10e Finite Mathematics with Applications 10e Copyright ©2011 Pearson Education, Inc. All right.

Counting Methods and Probability Theory

Counting Methods and Probability Theory

Presentation transcript:

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

© 2010 Pearson Prentice Hall. All rights reserved Probability with the Fundamental Counting Principle, Permutations, and Combinations

© 2010 Pearson Prentice Hall. All rights reserved. 3 Objectives 1.Compute probabilities with permutations. 2.Compute probabilities with combinations.

© 2010 Pearson Prentice Hall. All rights reserved. 4 Example 1: Probability and Permutations Six jokes about books by Groucho Marx, George Carlin, Steven Wright, Greg Ray, Jerry Seinfeld, and Phyllis Diller are each written on one of six cards. The cards are placed in a hat and drawn one at a time. What is the probability that a man’s joke will be delivered first and a woman’s joke last? Solution:

© 2010 Pearson Prentice Hall. All rights reserved. 5 Use the Fundamental Counting Principle to find the number of permutations with a man’s joke first and a woman’s joke last: Example 1: Probability and Permutations continued

© 2010 Pearson Prentice Hall. All rights reserved. 6 Example 2: Probability and Combinations: Winning the Lottery Florida’s lottery game, LOTTO, is set up so that each player chooses six different numbers from 1 to 53. With one LOTTO ticket, what is the probability of winning this prize? Solution: Because the order of the six numbers does not matter, this situation involves combinations.

© 2010 Pearson Prentice Hall. All rights reserved. 7 Example 3: Probability and Combinations A club consists of five men and seven women. Three members are selected at random to attend a conference. Find the probability that the selected group consists of 3 men. Solution: Order of selection does not matter, so this is a problem involving combinations.

© 2010 Pearson Prentice Hall. All rights reserved. 8 Example 3: Probability and Combinations continued A club consists of five men and seven women. Three members are selected at random to attend a conference. Find the probability that the selected group consists of 3 men. Solution: There are 220 possible three-person selections.

© 2010 Pearson Prentice Hall. All rights reserved. 9 Example 3: Probability and Combinations continued A club consists of five men and seven women. Three members are selected at random to attend a conference. Find the probability that the selected group consists of 3 men. Solution: Determine the numerator. We are interested in the number of ways of selecting three men from 5 men.