# Probability. Probabilty Impossibe Unlikely Equally Likely Likely Certain

Size: px
Start display at page:

Download "Probability. Probabilty Impossibe Unlikely Equally Likely Likely Certain"

Transcription

1 PROBABILITY

2 Probability The likelihood or chance of an event occurring If an event is IMPOSSIBLE its probability is ZERO If an event is CERTAIN its probability is ONE So all probabilities lie between 0 and 1 Probabilities can be represented as a fraction, decimal of percentages Probabilty Impossibe Unlikely Equally Likely Likely Certain

3 Experimental Probability Relative Frequency is an estimate of probability = Approaches theoretic probability as the number of trials increases Example Toss a coin 20 times an observe the relative frequency of getting tails.

4 Theoretical Probability Key Terms: Each EXPERIMENT has a given number of specific OUTCOMES which together make up the SAMPLE SPACE(S). The probability of an EVENT (A) occurring must be such that A is subset of S Experiment throwing coin die # possible Outcomes, n(s) 2 6 Sample Space, S H,T 1,2,3,4,5,6 Event A (A subset S) getting H getting even #

5 Theoretical Probability Probability The probability of an event A occurring is calculated as: Examples = ( ) = ( ) ( ) 1. A fair die is rolled find the probability of getting: a) a b) a factor of 6 c) a factor of 60 6 = =1 5 6 d) a number less than 6 e) a number greater than =0 A B 2. One letter is selected from excellent. Find the probability that it is: a) an e b) a consonant 3 9 = One card is selected from a deck of cards find the probability of selecting: a) a Queen b) a red card c) a red queen 4 52 = = = = 1 26

6 Theoretical Probability Conditional Probability Conditional Probability of A given B is the probability that A occurs given that event B has occurred. This basically changes the sample space to B Examples = ( ) ( ) 1. A fair die is rolled find the probability of getting: a) a 6 given that it is an even number b) a factor of 6, given that it is a factor of ,2} (1,2,4} 2 3 A B 2. One letter is selected from excellent. Find the probability that it is: a) a l given it is a consonant b) an e, given the letter is in excel 2 6 =1 3 {e,e,e} from {e,x,c,e,l,l,e} 3. One card is selected from a deck of cards find the probability of selecting: a) a Queen, given it is a face card b) a red card given it is a queen c) a queen, given it is red card 2 4 = = =1 3

7 Theoretical Probability Expectation The expectation of an event A is the number of times the event A is expected to occur within n number of trials, ( )= ( ) Examples 1. A coin is tossed 30 times. How many time would you expect to get tails? 30 =15 2. The probability that Mr Bennett wears a blue shirt on a given day is 15%. Find the expected number of days in September that he will wear a blue shirt? 15% 30=4.5 5

8 Sample Space Sample Space can be represented as: List Grid/Table Two-Way Table Venn Diagram Tree Diagram

9 Sample Space 1) LIST: Bag A: 1 Black, 1 white. Bag B: 1 Black, 1 Red One marble is selected from each bag. a) Represent the sample space as a LIST b) Hence state the probability of choosing the same colours ANSWER: =,,, = 1 4

10 Sample Space 2) i)grid: Two fair dice are rolled and the numbers noted a) Represent the sample space on a GRID b) Hence state the probability of choosing the same numbers ANSWER: = 6 5 Dice # P # = = 1 Dice #

11 Sample Space 2) ii)table: Two fair dice are rolled and the sum of the scores is recorded a) Represent the sample space in a TABLE b) Hence state the probability of getting an even sum ANSWER: = Dice 2\Dice P = =1 2

12 Sample Space 3) TWO- WAY TABLE: A survey of Grade 10 students at a small school returned the following results: Category Boys Girls Good at Math Not good at Math 8 12 A student is selected at random, find the probability that: a) it is a girl P = b) the student is not good at math c) it is a boy who is good at Math d) it is a girl, given the student is good at Math e) the student is good at Math, given that it is a girl = = 5 14 = = = 19 31

13 Sample Space 4) VENN DIAGRAM: The Venn diagram below shows sports played by students in a class: A student is selected at random, find the probability that the student: a) plays basket ball P = b) plays basket ball and tennis P & = 4 27 c) Plays basketball given that the student plays tennis P = 4 11

14 Sample Space 5) TREE DIAGRAM: Note: tree diagrams show outcomes and probabilities. The outcome is written at the end of each branch and the probability is written on each branch. Represent the following in tree diagrams: a) Two coins are tossed b) One marble is randomly selected from Bag A with 2 Black & 3 White marbles, then another is selected from Bag B with 5 Black & 2 Red marbles. c) The state allows each person to try for their pilot license a maximum of 3 times. The first time Mary goes the probability she passes is 45%, if she goes a second time the probability increases to 53% and on the third chance it increase to 58%.

15 Sample Space 5) TREE DIAGRAM: a) Answer:

16 Sample Space 5) TREE DIAGRAM: b) Answer:

17 Sample Space 5) TREE DIAGRAM: c) Answer:

18 Types of Events EXHAUSTIVE EVENTS: a set of event are said to be Exhaustive if together they represent the Sample Space. i.e A,B,C,D are exhaustive if: P(A)+P(B)+P(C)+P(D) = 1 Eg Fair Dice: P(1)+P(2)+P(3)+P(4)+P(5)+P(6)=

19 Types of Events COMPLEMENTARY EVENTS: two events are said to be complementary if one of them MUST occur. A, read as A complement is the event when A does not occur. A and A () are such that: P(A) + P(A ) = 1 State the complementary event for each of the following A A EVENT A Getting a 6 on a die Getting at least a 2 on a die Getting the same result when a coin is tossed twice A (COMPLEMENTARY EVENT) Eg Find the probability of not getting a 4 when a die is tossed P(4 ) = Eg. Find the probability that a card selected at random form a deck of cards is not a queen. P(Q )=

20 Types of Events COMPOUND EVENTS: EXCLUSIVE EVENTS: a set of event are said to be Exclusive (two events would be Mutually Excusive ) if they cannot occur together. i.e they are disjoint sets A B INDEPENDENT EVENTS: a set of event are said to be Independent if the occurrence of one DOES NOT affect the other. DEPENDENT EVENTS: a set of event are said to be dependent if the occurrence of one DOES affect the other.

21 Types of Events EXCLUSIVE/ INDEPENDENT / DEPENDENT EVENTS Which of the following pairs are mutually exclusive events? Event A Getting an A* in IGCSE Math Exam Leslie getting to school late Abi waking up late Getting a Head on toss 1 of a coin Getting a Head on toss 1 of a coin Which of the following pairs are dependent/independent events? Event A Getting a Head on toss 1 of a coin Alvin studying for his exams Racquel getting an A* in Math Abi waking up late Taking Additional Math Event B Getting an E in IGCSE Math Exam Leslie getting to school on time Abi getting to school on time Getting a Tail on toss 1 of a coin Getting a Tail on toss 2 of a coin Event B Getting a Tail on toss 2 of a coin Alvin doing well in his exams Racquel getting an A* in Art Abi getting to school on time Taking Higher Level Math

22 Probabilities of Compound Events Type of Probability AND OR When combining events, one event may or may not have an effect on the other, which may in turn affect related probabilities Meaning Diagram Calculation Probability that event A AND event B will occur together. Generally, AND = multiplication Probability that either event A OR event B (or both) will occur. Generally, OR = addition A A B B = Note: For Exclusive Events: since they cannot occur together then, = For Independent: Events: since A is not affected by the occurrence of B = A = + B Note: For Exclusive Events: since such events are disjoint sets, = +

23 Examples Using Complementary Probability 1. The table below show grades of students is a Math Quiz Grade Frequency Find the probability that a student selected at random scored at least 2 on the quiz (i)by Theoretical Probability (ii) By Complementary

24

25 Examples Using OR Probability 1. A fair die is rolled, find the probability of getting a 3 or a 5. (i)by Sample Space (ii) By OR rule

26

27 Examples Using AND Probability 1. A fair die is rolled twice find the probability of getting a 5 and a 5. (i)by Sample Space (ii) By AND rule

28

29 Examples Using OR / AND Probability 1. A fair die is rolled twice find the probability of getting a 3 and a 5. (i)by Sample Space (ii) By AND/OR rule

30

31 Mixed Examples 1. From a pack of playing cards, 1 card is selected. Find the probability of selecting: a) A queen or a king b) Heart or diamond c) A queen or a heart = =1 2 P(Q)+P(H)-P(Q&H)= + = d) A queen given that at face card was selected 4 12 =1 3 e) A card that has a value of at least 3 (if face cards have a value of 10 and Ace has a value of 1) == 4 52

32 Mixed Examples 2. From a pack of playing cards, 1 card is selected noted and replaced, then a 2 nd card is selected and noted. Find the probability of selecting: a) A queen and then a king b) A queen and a king c) Two cards of same number = P(Q&K) or P(K&Q)= 2 P(A&A) or P(2&2) or.pk&k) = 13= d) Two different cards 1-P(same) =1 =

33 Mixed Examples 3. From a pack of playing cards, 1 card is selected noted, it is NOT replaced, then a 2 nd card is selected and noted. Find the probability of selecting: a) A queen and then a king b) A queen and a king c) Two cards of same number d) Two cards with different numbers

34 Probabilities of Repeated Events 1) A coin is tossed 3 times find the probability of getting: a) tail exactly once a) a tail AT LEAST once 2) A die is tossed until a 6 appears. Find the probability of getting a 6: a) on the 2 nd toss b) on the 3 rd toss c) on the n th toss

35 Tree Diagrams 1. A die is tossed twice. Draw a tree diagram and find the probability of getting and even number and an odd number.

36 1. Tree Diagrams

37 Tree Diagrams 2. i) Find the probability that: a) he is on time for school b) he is on time everyday in a 5 day week c) he is on time once in a 5 day week ii)if there are 60 days this term, how many days would you expect Jack to be late this term?

38 Tree Diagrams 2. i) a) b) c) ii)

39 Tree Diagrams 3.

40 Tree Diagrams 3a).

41 Tree Diagrams 3b)

### Probability. Ms. Weinstein Probability & Statistics

Probability Ms. Weinstein Probability & Statistics Definitions Sample Space The sample space, S, of a random phenomenon is the set of all possible outcomes. Event An event is a set of outcomes of a random

More information

### PROBABILITY. 1. Introduction. Candidates should able to:

PROBABILITY Candidates should able to: evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g for the total score when two fair dice are thrown), or by calculation

More information

### 7.1 Experiments, Sample Spaces, and Events

7.1 Experiments, Sample Spaces, and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment

More information

### 4.1 Sample Spaces and Events

4.1 Sample Spaces and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment is called an

More information

### PROBABILITY M.K. HOME TUITION. Mathematics Revision Guides. Level: GCSE Foundation Tier

Mathematics Revision Guides Probability Page 1 of 18 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier PROBABILITY Version: 2.1 Date: 08-10-2015 Mathematics Revision Guides Probability

More information

### LC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following.

A Ryan LC OL Probability ARNMaths.weebly.com Learning Outcomes As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. Counting List outcomes of an experiment Apply

More information

### Grade 6 Math Circles Fall Oct 14/15 Probability

1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2014 - Oct 14/15 Probability Probability is the likelihood of an event occurring.

More information

### ECON 214 Elements of Statistics for Economists

ECON 214 Elements of Statistics for Economists Session 4 Probability Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education School of Continuing

More information

### Math 1313 Section 6.2 Definition of Probability

Math 1313 Section 6.2 Definition of Probability Probability is a measure of the likelihood that an event occurs. For example, if there is a 20% chance of rain tomorrow, that means that the probability

More information

### Section Introduction to Sets

Section 1.1 - Introduction to Sets Definition: A set is a well-defined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase

More information

### Independent Events B R Y

. Independent Events Lesson Objectives Understand independent events. Use the multiplication rule and the addition rule of probability to solve problems with independent events. Vocabulary independent

More information

### Chapter 3: PROBABILITY

Chapter 3 Math 3201 1 3.1 Exploring Probability: P(event) = Chapter 3: PROBABILITY number of outcomes favourable to the event total number of outcomes in the sample space An event is any collection of

More information

### Intermediate Math Circles November 1, 2017 Probability I

Intermediate Math Circles November 1, 2017 Probability I Probability is the study of uncertain events or outcomes. Games of chance that involve rolling dice or dealing cards are one obvious area of application.

More information

### Def: The intersection of A and B is the set of all elements common to both set A and set B

Def: Sample Space the set of all possible outcomes Def: Element an item in the set Ex: The number "3" is an element of the "rolling a die" sample space Main concept write in Interactive Notebook Intersection:

More information

### Chapter 1: Sets and Probability

Chapter 1: Sets and Probability Section 1.3-1.5 Recap: Sample Spaces and Events An is an activity that has observable results. An is the result of an experiment. Example 1 Examples of experiments: Flipping

More information

### CSC/MATA67 Tutorial, Week 12

CSC/MATA67 Tutorial, Week 12 November 23, 2017 1 More counting problems A class consists of 15 students of whom 5 are prefects. Q: How many committees of 8 can be formed if each consists of a) exactly

More information

### Name: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11

Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value

More information

### Probability. Dr. Zhang Fordham Univ.

Probability! Dr. Zhang Fordham Univ. 1 Probability: outline Introduction! Experiment, event, sample space! Probability of events! Calculate Probability! Through counting! Sum rule and general sum rule!

More information

### Such a description is the basis for a probability model. Here is the basic vocabulary we use.

5.2.1 Probability Models When we toss a coin, we can t know the outcome in advance. What do we know? We are willing to say that the outcome will be either heads or tails. We believe that each of these

More information

### Chapter 4: Probability and Counting Rules

Chapter 4: Probability and Counting Rules Before we can move from descriptive statistics to inferential statistics, we need to have some understanding of probability: Ch4: Probability and Counting Rules

More information

### Unit 7 Central Tendency and Probability

Name: Block: 7.1 Central Tendency 7.2 Introduction to Probability 7.3 Independent Events 7.4 Dependent Events 7.1 Central Tendency A central tendency is a central or value in a data set. We will look at

More information

### I. WHAT IS PROBABILITY?

C HAPTER 3 PROAILITY Random Experiments I. WHAT IS PROAILITY? The weatherman on 10 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and

More information

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Study Guide for Test III (MATH 1630) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the number of subsets of the set. 1) {x x is an even

More information

### Define and Diagram Outcomes (Subsets) of the Sample Space (Universal Set)

12.3 and 12.4 Notes Geometry 1 Diagramming the Sample Space using Venn Diagrams A sample space represents all things that could occur for a given event. In set theory language this would be known as the

More information

### When a number cube is rolled once, the possible numbers that could show face up are

C3 Chapter 12 Understanding Probability Essential question: How can you describe the likelihood of an event? Example 1 Likelihood of an Event When a number cube is rolled once, the possible numbers that

More information

### Unit 1 Day 1: Sample Spaces and Subsets. Define: Sample Space. Define: Intersection of two sets (A B) Define: Union of two sets (A B)

Unit 1 Day 1: Sample Spaces and Subsets Students will be able to (SWBAT) describe events as subsets of sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,

More information

### Outcomes: The outcomes of this experiment are yellow, blue, red and green.

(Adapted from http://www.mathgoodies.com/) 1. Sample Space The sample space of an experiment is the set of all possible outcomes of that experiment. The sum of the probabilities of the distinct outcomes

More information

### 13-6 Probabilities of Mutually Exclusive Events

Determine whether the events are mutually exclusive or not mutually exclusive. Explain your reasoning. 1. drawing a card from a standard deck and getting a jack or a club The jack of clubs is an outcome

More information

### Before giving a formal definition of probability, we explain some terms related to probability.

probability 22 INTRODUCTION In our day-to-day life, we come across statements such as: (i) It may rain today. (ii) Probably Rajesh will top his class. (iii) I doubt she will pass the test. (iv) It is unlikely

More information

### Probability Test Review Math 2. a. What is? b. What is? c. ( ) d. ( )

Probability Test Review Math 2 Name 1. Use the following venn diagram to answer the question: Event A: Odd Numbers Event B: Numbers greater than 10 a. What is? b. What is? c. ( ) d. ( ) 2. In Jason's homeroom

More information

### Unit 11 Probability. Round 1 Round 2 Round 3 Round 4

Study Notes 11.1 Intro to Probability Unit 11 Probability Many events can t be predicted with total certainty. The best thing we can do is say how likely they are to happen, using the idea of probability.

More information

### Worksheets for GCSE Mathematics. Probability. mr-mathematics.com Maths Resources for Teachers. Handling Data

Worksheets for GCSE Mathematics Probability mr-mathematics.com Maths Resources for Teachers Handling Data Probability Worksheets Contents Differentiated Independent Learning Worksheets Probability Scales

More information

### Probability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College

Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical

More information

### Key Concepts. Theoretical Probability. Terminology. Lesson 11-1

Key Concepts Theoretical Probability Lesson - Objective Teach students the terminology used in probability theory, and how to make calculations pertaining to experiments where all outcomes are equally

More information

### Probability. The Bag Model

Probability The Bag Model Imagine a bag (or box) containing balls of various kinds having various colors for example. Assume that a certain fraction p of these balls are of type A. This means N = total

More information

### Probability Rules. 2) The probability, P, of any event ranges from which of the following?

Name: WORKSHEET : Date: Answer the following questions. 1) Probability of event E occurring is... P(E) = Number of ways to get E/Total number of outcomes possible in S, the sample space....if. 2) The probability,

More information

### Bellwork Write each fraction as a percent Evaluate P P C C 6

Bellwork 2-19-15 Write each fraction as a percent. 1. 2. 3. 4. Evaluate. 5. 6 P 3 6. 5 P 2 7. 7 C 4 8. 8 C 6 1 Objectives Find the theoretical probability of an event. Find the experimental probability

More information

### Math Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.

Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166 - Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 7.1 - Experiments, Sample Spaces,

More information

### Math Exam 2 Review. NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5.

Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166 - Exam 2 Review NOTE: For reviews of the other sections on Exam 2, refer to the first page of WIR #4 and #5. Section 7.1 - Experiments, Sample Spaces,

More information

### Grade 7/8 Math Circles February 25/26, Probability

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Probability Grade 7/8 Math Circles February 25/26, 2014 Probability Centre for Education in Mathematics and Computing Probability is the study of how likely

More information

### , x {1, 2, k}, where k > 0. (a) Write down P(X = 2). (1) (b) Show that k = 3. (4) Find E(X). (2) (Total 7 marks)

1. The probability distribution of a discrete random variable X is given by 2 x P(X = x) = 14, x {1, 2, k}, where k > 0. Write down P(X = 2). (1) Show that k = 3. Find E(X). (Total 7 marks) 2. In a game

More information

### RANDOM EXPERIMENTS AND EVENTS

Random Experiments and Events 18 RANDOM EXPERIMENTS AND EVENTS In day-to-day life we see that before commencement of a cricket match two captains go for a toss. Tossing of a coin is an activity and getting

More information

### Module 4 Project Maths Development Team Draft (Version 2)

5 Week Modular Course in Statistics & Probability Strand 1 Module 4 Set Theory and Probability It is often said that the three basic rules of probability are: 1. Draw a picture 2. Draw a picture 3. Draw

More information

### November 6, Chapter 8: Probability: The Mathematics of Chance

Chapter 8: Probability: The Mathematics of Chance November 6, 2013 Last Time Crystallographic notation Groups Crystallographic notation The first symbol is always a p, which indicates that the pattern

More information

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Statistics Homework Ch 5 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability

More information

### 7 5 Compound Events. March 23, Alg2 7.5B Notes on Monday.notebook

7 5 Compound Events At a juice bottling factory, quality control technicians randomly select bottles and mark them pass or fail. The manager randomly selects the results of 50 tests and organizes the data

More information

### (a) Suppose you flip a coin and roll a die. Are the events obtain a head and roll a 5 dependent or independent events?

Unit 6 Probability Name: Date: Hour: Multiplication Rule of Probability By the end of this lesson, you will be able to Understand Independence Use the Multiplication Rule for independent events Independent

More information

### Probability - Grade 10 *

OpenStax-CNX module: m32623 1 Probability - Grade 10 * Rory Adams Free High School Science Texts Project Sarah Blyth Heather Williams This work is produced by OpenStax-CNX and licensed under the Creative

More information

### Section 7.3 and 7.4 Probability of Independent Events

Section 7.3 and 7.4 Probability of Independent Events Grade 7 Review Two or more events are independent when one event does not affect the outcome of the other event(s). For example, flipping a coin and

More information

### Probability and Counting Rules. Chapter 3

Probability and Counting Rules Chapter 3 Probability as a general concept can be defined as the chance of an event occurring. Many people are familiar with probability from observing or playing games of

More information

### Basic Probability Ideas. Experiment - a situation involving chance or probability that leads to results called outcomes.

Basic Probability Ideas Experiment - a situation involving chance or probability that leads to results called outcomes. Random Experiment the process of observing the outcome of a chance event Simulation

More information

### The point value of each problem is in the left-hand margin. You must show your work to receive any credit, except on problems 1 & 2. Work neatly.

Introduction to Statistics Math 1040 Sample Exam II Chapters 5-7 4 Problem Pages 4 Formula/Table Pages Time Limit: 90 Minutes 1 No Scratch Paper Calculator Allowed: Scientific Name: The point value of

More information

### Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes

Worksheet 6 th Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of

More information

### STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving.

Worksheet 4 th Topic : PROBABILITY TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving. BASIC COMPETENCY:

More information

### Find the probability of an event by using the definition of probability

LESSON 10-1 Probability Lesson Objectives Find the probability of an event by using the definition of probability Vocabulary experiment (p. 522) trial (p. 522) outcome (p. 522) sample space (p. 522) event

More information

### Normal Distribution Lecture Notes Continued

Normal Distribution Lecture Notes Continued 1. Two Outcome Situations Situation: Two outcomes (for against; heads tails; yes no) p = percent in favor q = percent opposed Written as decimals p + q = 1 Why?

More information

### Name Date. Probability of Disjoint and Overlapping Events For use with Exploration 12.4

12.4 Probability of Disjoint and Overlapping Events For use with Exploration 12.4 Essential Question How can you find probabilities of disjoint and overlapping events? Two events are disjoint, or mutually

More information

### Probability: introduction

May 6, 2009 Probability: introduction page 1 Probability: introduction Probability is the part of mathematics that deals with the chance or the likelihood that things will happen The probability of an

More information

### Basic Probability. Let! = # 8 # < 13, # N -,., and / are the subsets of! such that - = multiples of four. = factors of 24 / = square numbers

Basic Probability Let! = # 8 # < 13, # N -,., and / are the subsets of! such that - = multiples of four. = factors of 24 / = square numbers (a) List the elements of!. (b) (i) Draw a Venn diagram to show

More information

### Name: 1. Match the word with the definition (1 point each - no partial credit!)

Chapter 12 Exam Name: Answer the questions in the spaces provided. If you run out of room, show your work on a separate paper clearly numbered and attached to this exam. SHOW ALL YOUR WORK!!! Remember

More information

### This unit will help you work out probability and use experimental probability and frequency trees. Key points

Get started Probability This unit will help you work out probability and use experimental probability and frequency trees. AO Fluency check There are 0 marbles in a bag. 9 of the marbles are red, 7 are

More information

### Review. Natural Numbers: Whole Numbers: Integers: Rational Numbers: Outline Sec Comparing Rational Numbers

FOUNDATIONS Outline Sec. 3-1 Gallo Name: Date: Review Natural Numbers: Whole Numbers: Integers: Rational Numbers: Comparing Rational Numbers Fractions: A way of representing a division of a whole into

More information

### ABC High School, Kathmandu, Nepal. Topic : Probability

BC High School, athmandu, Nepal Topic : Probability Grade 0 Teacher: Shyam Prasad charya. Objective of the Module: t the end of this lesson, students will be able to define and say formula of. define Mutually

More information

### 1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 100 calculators is tested.

1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 0 calculators is tested. Write down the expected number of faulty calculators in the sample. Find

More information

### What Do You Expect? Concepts

Important Concepts What Do You Expect? Concepts Examples Probability A number from 0 to 1 that describes the likelihood that an event will occur. Theoretical Probability A probability obtained by analyzing

More information

### If you roll a die, what is the probability you get a four OR a five? What is the General Education Statistics

If you roll a die, what is the probability you get a four OR a five? What is the General Education Statistics probability that you get neither? Class Notes The Addition Rule (for OR events) and Complements

More information

### MEP Practice Book SA5

5 Probability 5.1 Probabilities MEP Practice Book SA5 1. Describe the probability of the following events happening, using the terms Certain Very likely Possible Very unlikely Impossible (d) (e) (f) (g)

More information

### Bell Work. Warm-Up Exercises. Two six-sided dice are rolled. Find the probability of each sum or 7

Warm-Up Exercises Two six-sided dice are rolled. Find the probability of each sum. 1. 7 Bell Work 2. 5 or 7 3. You toss a coin 3 times. What is the probability of getting 3 heads? Warm-Up Notes Exercises

More information

### 4.3 Finding Probability Using Sets

4.3 Finding Probability Using ets When rolling a die with sides numbered from 1 to 20, if event A is the event that a number divisible by 5 is rolled: a) What is the sample space,? b) What is the event

More information

### Probability. Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible

Probability Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible Impossible In summer, it doesn t rain much in Cape Town, so on a chosen

More information

### STATISTICS and PROBABILITY GRADE 6

Kansas City Area Teachers of Mathematics 2016 KCATM Math Competition STATISTICS and PROBABILITY GRADE 6 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes You may use

More information

### Independent and Mutually Exclusive Events

Independent and Mutually Exclusive Events By: OpenStaxCollege Independent and mutually exclusive do not mean the same thing. Independent Events Two events are independent if the following are true: P(A

More information

### 5.6. Independent Events. INVESTIGATE the Math. Reflecting

5.6 Independent Events YOU WILL NEED calculator EXPLORE The Fortin family has two children. Cam determines the probability that the family has two girls. Rushanna determines the probability that the family

More information

### COMPOUND EVENTS. Judo Math Inc.

COMPOUND EVENTS Judo Math Inc. 7 th grade Statistics Discipline: Black Belt Training Order of Mastery: Compound Events 1. What are compound events? 2. Using organized Lists (7SP8) 3. Using tables (7SP8)

More information

### Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results:

Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results: Outcome Frequency 1 8 2 8 3 12 4 7 5 15 8 7 8 8 13 9 9 10 12 (a) What is the experimental probability

More information

### CHAPTER 7 Probability

CHAPTER 7 Probability 7.1. Sets A set is a well-defined collection of distinct objects. Welldefined means that we can determine whether an object is an element of a set or not. Distinct means that we can

More information

### Probability Assignment

Name Probability Assignment Student # Hr 1. An experiment consists of spinning the spinner one time. a. How many possible outcomes are there? b. List the sample space for the experiment. c. Determine the

More information

### Probability - Chapter 4

Probability - Chapter 4 In this chapter, you will learn about probability its meaning, how it is computed, and how to evaluate it in terms of the likelihood of an event actually happening. A cynical person

More information

### Part 1: I can express probability as a fraction, decimal, and percent

Name: Pattern: Part 1: I can express probability as a fraction, decimal, and percent For #1 to #4, state the probability of each outcome. Write each answer as a) a fraction b) a decimal c) a percent Example:

More information

### Fdaytalk.com. Outcomes is probable results related to an experiment

EXPERIMENT: Experiment is Definite/Countable probable results Example: Tossing a coin Throwing a dice OUTCOMES: Outcomes is probable results related to an experiment Example: H, T Coin 1, 2, 3, 4, 5, 6

More information

### Section Theoretical and Experimental Probability...Wks 3

Name: Class: Date: Section 6.8......Theoretical and Experimental Probability...Wks 3. Eight balls numbered from to 8 are placed in a basket. One ball is selected at random. Find the probability that it

More information

### Probability. Chapter-13

Chapter-3 Probability The definition of probability was given b Pierre Simon Laplace in 795 J.Cardan, an Italian physician and mathematician wrote the first book on probability named the book of games

More information

### 4.1 What is Probability?

4.1 What is Probability? between 0 and 1 to indicate the likelihood of an event. We use event is to occur. 1 use three major methods: 1) Intuition 3) Equally Likely Outcomes Intuition - prediction based

More information

### Math 7 Notes - Unit 11 Probability

Math 7 Notes - Unit 11 Probability Probability Syllabus Objective: (7.2)The student will determine the theoretical probability of an event. Syllabus Objective: (7.4)The student will compare theoretical

More information

### Name. Is the game fair or not? Prove your answer with math. If the game is fair, play it 36 times and record the results.

Homework 5.1C You must complete table. Use math to decide if the game is fair or not. If Period the game is not fair, change the point system to make it fair. Game 1 Circle one: Fair or Not 2 six sided

More information

### Math 1070 Sample Exam 1

University of Connecticut Department of Mathematics Math 1070 Sample Exam 1 Exam 1 will cover sections 4.1-4.7 and 5.1-5.4. This sample exam is intended to be used as one of several resources to help you

More information

### Probability 1. Joseph Spring School of Computer Science. SSP and Probability

Probability 1 Joseph Spring School of Computer Science SSP and Probability Areas for Discussion Experimental v Theoretical Probability Looking Back v Looking Forward Theoretical Probability Sample Space,

More information

### Probability MAT230. Fall Discrete Mathematics. MAT230 (Discrete Math) Probability Fall / 37

Probability MAT230 Discrete Mathematics Fall 2018 MAT230 (Discrete Math) Probability Fall 2018 1 / 37 Outline 1 Discrete Probability 2 Sum and Product Rules for Probability 3 Expected Value MAT230 (Discrete

More information

### Math 227 Elementary Statistics. Bluman 5 th edition

Math 227 Elementary Statistics Bluman 5 th edition CHAPTER 4 Probability and Counting Rules 2 Objectives Determine sample spaces and find the probability of an event using classical probability or empirical

More information

### 1. How to identify the sample space of a probability experiment and how to identify simple events

Statistics Chapter 3 Name: 3.1 Basic Concepts of Probability Learning objectives: 1. How to identify the sample space of a probability experiment and how to identify simple events 2. How to use the Fundamental

More information

### Georgia Department of Education Georgia Standards of Excellence Framework GSE Geometry Unit 6

How Odd? Standards Addressed in this Task MGSE9-12.S.CP.1 Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not). MGSE9-12.S.CP.7

More information

### Objective: Determine empirical probability based on specific sample data. (AA21)

Do Now: What is an experiment? List some experiments. What types of things does one take a "chance" on? Mar 1 3:33 PM Date: Probability - Empirical - By Experiment Objective: Determine empirical probability

More information

### Section 6.5 Conditional Probability

Section 6.5 Conditional Probability Example 1: An urn contains 5 green marbles and 7 black marbles. Two marbles are drawn in succession and without replacement from the urn. a) What is the probability

More information

### Probability Models. Section 6.2

Probability Models Section 6.2 The Language of Probability What is random? Empirical means that it is based on observation rather than theorizing. Probability describes what happens in MANY trials. Example

More information

### MEP Practice Book ES5. 1. A coin is tossed, and a die is thrown. List all the possible outcomes.

5 Probability MEP Practice Book ES5 5. Outcome of Two Events 1. A coin is tossed, and a die is thrown. List all the possible outcomes. 2. A die is thrown twice. Copy the diagram below which shows all the

More information

### Chapter 1 - Set Theory

Midterm review Math 3201 Name: Chapter 1 - Set Theory Part 1: Multiple Choice : 1) U = {hockey, basketball, golf, tennis, volleyball, soccer}. If B = {sports that use a ball}, which element would be in

More information

### Probability is the likelihood that an event will occur.

Section 3.1 Basic Concepts of is the likelihood that an event will occur. In Chapters 3 and 4, we will discuss basic concepts of probability and find the probability of a given event occurring. Our main

More information

### Essential Question How can you list the possible outcomes in the sample space of an experiment?

. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G..B Sample Spaces and Probability Essential Question How can you list the possible outcomes in the sample space of an experiment? The sample space of an experiment

More information

### Use this information to answer the following questions.

1 Lisa drew a token out of the bag, recorded the result, and then put the token back into the bag. She did this 30 times and recorded the results in a bar graph. Use this information to answer the following

More information

### Exercise Class XI Chapter 16 Probability Maths

Exercise 16.1 Question 1: Describe the sample space for the indicated experiment: A coin is tossed three times. A coin has two faces: head (H) and tail (T). When a coin is tossed three times, the total

More information