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.

Slides:

Advertisements

Similar presentations

4.3 Conditional Probability

Advertisements

Unit 4 – Combinatorics and Probability Section 4.3 – An Introduction to Probability Calculator Required.

1 Counting Problems From Fred Greenleaf’s QR book Compiled by Samuel Marateck.

Chapter 13 sec. 3.  Def.  Is an ordering of distinct objects in a straight line. If we select r different objects from a set of n objects and arrange.

16.4 Probability Problems Solved with Combinations.

Chapter 4 Probability and Counting Rules Section 4-2

Chapter 7 - Part Two Counting Techniques Wednesday, March 18, 2009.

Laws of Probability What is the probability of throwing a pair of dice and obtaining a 5 or a 7? These are mutually exclusive events. You can’t throw.

Probability Using Permutations and Combinations

Permutations and Combinations

Probability Jeopardy Final Jeopardy Simple Probabilities Permutations or Combinations Counting Principle Find the Probability Independent Dependent Q.

Unit 4 – Combinatorics and Probability Section 4.4 – Probability with Combinations Calculator Required.

Permutations and Combinations. Random Things to Know.

Probability and Counting Rules

Chapter 8 Counting Principles: Further Probability Topics Section 8.2 Combinations.

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

Permutations and Combinations

Counting. Product Rule Example Sum Rule Pigeonhole principle If there are more pigeons than pigeonholes, then there must be at least one pigeonhole.

Chapter 5: Introduction to Probability 5.3 Counting and theoretical probabilities: How many? 1 Learning Objectives:  Learn how to count outcomes without.

Section 14.4 – Probability and Odds. Probability = compute first number of winnerscompute second Ratios reduce like fractions.

13.3 Probability and Odds What is the probability of rolling a 5 on a die? What is the probability of drawing a 4 from a deck of playing cards? Warm Up.

Unit 4 Section : Probability and Counting Rules  Counting rules can be combined with probability rules to solve many types of probability problems.

COUNTING RULES PROBLEMS 1. How many different ways can a nurse visit 9 patients if she wants to visit them all in one day? If she wants to visit only 5?

Conditional Probability CHAPTER 4.3. INTRO TO VENN DIAGRAMS - PETS.

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

Aim: How do we use permutations and combinations to solve probability problems? Do Now: Six students are arranged at random on a bench. What is the probability.

Notes Over 12.3 Finding Probabilities of Events

Part 2 – Factorial and other Counting Rules

Chapter 12 – Probability and Statistics 12.2 – Permutations and Combinations.

Section 11.4 Tree Diagrams, Tables, and Sample Spaces Math in Our World.

Permutations and Combinations Advanced Math Topics.

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.

Probability and Statistics

Combinations and Permutations CHAPTER 4.4.  Permutations are used when arranging r out of n items in a specific order. n P r = PERMUTATIONS.

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.

7.3 Combinations Math A combination is a selection of a group of objects taken from a larger pool for which the kinds of objects selected is of.

8.6 Counting Principles. Listing Possibilities: Ex 1 Eight pieces of paper are numbered from 1 to 8 and placed in a box. One piece of paper is drawn from.

5.5 Generalized Permutations and Combinations

Skip Counting Practice

Lecturer : FATEN AL-HUSSAIN

Introduction to probability (2) Combinations التوافيق Definition of combination: It is a way of selecting items from a collection, such that the order.

Addition Rules for Probability.  Two events are mutually exclusive events if they cannot occur at the same time (i.e., they have no outcomes in common)

Sample Spaces and Probability Addition Rules Multiplication Rules and Conditional Probability Counting Rules Probability and Counting Rules

CHAPTER 4 4-4:Counting Rules Instructor: Alaa saud Note: This PowerPoint is only a summary and your main source should be the book.

MATHPOWER TM 12, WESTERN EDITION Chapter 8 Probability

Chapter # 4 Probability and Counting Rules. 4-1 Sample Spaces and Probability 4-2 Addition Rules for Probability 4-3 Multiplication Rules & Conditional.

Section The Product Rule  Example: How many different license plates can be made if each plate contains a sequence of three uppercase English letters.

Pre-Calculus Section 8.6A Counting Principles. 1. Eight pieces of paper are numbered 1 to 8 and placed in a box. One piece of paper is drawn from the.

Section 6.3. Section Summary Permutations Combinations.

© 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.

4-1 Chapter 4 Counting Techniques.

Probability and Combinatorics

Probability and Counting Rules

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.

4-1 Chapter 4 Counting Techniques.

Warm Up Evaluate  4  3  2   6  5  4  3  2  1

4-1 Chapter 4 Counting Techniques.

3.4 The Binomial Distribution

Permutation – The number of ways to ARRANGE ‘n’ items ‘r’ at

Warm Up Which of the following are combinations?

Counting Methods and Probability Theory

Combination and Permutations Quiz!

Monday May 1, 2017 A political discussion group consists of 5 Democrats and 6 Republicans. Four people are selected to attend a conference. In how many.

4-1 Chapter 4 Counting Techniques.

Counting Methods and Probability Theory

Presentation transcript:

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 ACES

 A box contains 24 transistors, four of which are defective. If four are sold at random, find the following probabilities: a.Exactly two are defective b.None are defective c.All are defective d.At least one is defective DEFECTIVE TRANSISTORS

 A store has six TV Graphic magazines and eight Newstime magazines on the counter. If two customers purchased a magazine, find the probability that one of each magazine was purchased. MAGAZINES

 A combination lock consists of the twenty six letters of the alphabet. If a three letter combination is needed, find the probability that the combination of the letters ABC in that order. The same letter can be used more than once. (Note: a combination lock is really a permutation lock) COMBINATION LOCK

 There are eight married couples in a tennis club. If one man and one woman are selected at random to plan the summer tournament, find the probability that they are married to each other. TENNIS TOURNAMENT

 Pg. 247 #1-8 APPLYING THE CONCEPTS