Khushboo Khanna, profile picture
Uploaded byKhushboo Khanna
PPT, PDF4,091 views

Chapter 4- probability

This document provides an overview of probability concepts including: - Probability is the chance of an event occurring and is calculated using the classical or empirical formulas - Events can be simple, compound, mutually exclusive or complementary - The addition rule states that for mutually exclusive events the probability of event A or B is P(A) + P(B), and for non-mutually exclusive events it is P(A) + P(B) - P(A and B) - The multiplication rule states that if events are independent, the probability of both occurring is P(A) × P(B) - Conditional probability is the probability of one event occurring given that another event has occurred - Examples are provided to

Embed presentation

Downloaded 42 times
1 / 109
2 / 109
3 / 109
4 / 109
5 / 109
6 / 109
7 / 109
8 / 109
9 / 109
10 / 109
11 / 109
12 / 109
13 / 109
14 / 109
15 / 109
16 / 109
17 / 109
18 / 109
19 / 109
20 / 109
21 / 109
22 / 109
23 / 109
24 / 109
25 / 109
26 / 109
27 / 109
28 / 109
29 / 109
30 / 109
31 / 109
32 / 109
33 / 109
34 / 109
35 / 109
36 / 109
37 / 109
38 / 109
39 / 109
40 / 109
41 / 109
42 / 109
43 / 109
44 / 109
45 / 109
46 / 109
47 / 109
48 / 109
49 / 109
50 / 109
51 / 109
52 / 109
53 / 109
54 / 109
55 / 109
56 / 109
57 / 109
58 / 109
59 / 109
60 / 109
61 / 109
62 / 109
63 / 109
64 / 109
65 / 109
66 / 109
67 / 109
68 / 109
69 / 109
70 / 109
71 / 109
72 / 109
73 / 109
74 / 109
75 / 109
76 / 109
77 / 109
78 / 109
79 / 109
80 / 109
81 / 109
82 / 109
83 / 109
84 / 109
85 / 109
86 / 109
87 / 109
88 / 109
89 / 109
90 / 109
91 / 109
92 / 109
93 / 109
94 / 109
95 / 109
96 / 109
97 / 109
98 / 109
99 / 109
100 / 109
101 / 109
102 / 109
103 / 109
104 / 109
105 / 109
106 / 109
107 / 109
108 / 109
109 / 109
Chapter 4: Probability
Probability • Probability is the chance of an event occurring. • A probability experiment is a chance process that leads to well-defined results called outcomes. • An outcome is the result of a single trial of a probability experiment.
• A sample space is the set of all possible outcomes of a probability experiment.
Example • Find the sample space for tossing two coins. • Find the sample space for tossing a coin and rolling a die.
Example • Use a tree diagram to determine the outcomes of an experiment of tossing three coins.
• An event is a set of outcomes. An event can be one outcome or more than one outcome. • An event with one outcome is called a simple event. • An event with more than one outcome is called a compound event.
Example • The event of drawing a card and getting a queen of hearts is a _____________ event. • The event of drawing a card and getting a spade is a ____________ event
• Classical probability uses sample spaces to determine the numerical probability that an event will happen. • Classical probability assumes that all outcomes in the sample space are equally likely to occur.
Formula for Classical Probability – • The probability of any event E is _________________________________ _____ = ________
• Example: If a die is rolled one time, find these probabilities. a) of getting a 4 • b) of getting an even number • c) of getting a number greater than 4 • d) of getting a number greater than 3 and an odd number
Probability Rules • The probability of an event E is a number between and including 0 and 1. 0 < P(E) < 1 • If an event E cannot occur, its probability is 0. • If an event E is certain to occur its probability is 1. • The sum of the probabilities of the outcomes in a sample space is 1.
Complementary Events • The complement of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by _______.
Example • Find the complement of each event. • Flipping two coins and getting at least one head • Selecting a day of the week that has two syllables.
Example • Find the complement of each event. – Rolling a die and getting a number greater than 4 – Drawing a card and getting a face card
Rule for Complementary Events • _______________ • • • or __________________ or _______________
Examples • An urn contains three red marbles, eight white marbles and 3 green marbles. Find the probability of selecting a marble that is not green. • Two dice are tossed. Find the probability of not getting doubles.
Classical vs. Empirical Probability • The difference between classical and empirical probability is that classical probability assumes that certain outcomes are equally likely while empirical probability relies on actual observation to determine the likelihood of outcomes.
Formula for Empirical Probability • Given a frequency distribution the probability of an event being in a given class is _____= ___________________________ =_______ • This probability is called empirical probability and is based on observation.
Example: • The director of the Readlot College Health Center wishes to open an eye clinic. To justify the expense of such a clinic, the director reports the probability that a student selected at random from the college roster needs corrective lenses. He took a random sample of 500 students to compute this probability and found that 375 of them need corrective lenses. What is the probability that a Readlot College student selected at random needs corrective lenses?
Example • The Right to Health Lobby wants to make a claim about the number of erroneous reports issued by a medical lab in one low-cost health center. Suppose they find in a random sample of 100 reports, 40 erroneous lab reports. What’s the probability that a report issued by this health center is erroneous?
Law of Large Numbers • As the number of trials increases the empirical probability will approach the theoretical probability.
Subjective Probability • Subjective probability uses a probability value based on an educated guess or estimate, employing opinions and inexact information.
Example • Example: Classify each statement as an example of classical probability, empirical probability, or subjective probability. • The probability that a person will watch the 6:00 news. • The probability of winning at a chuck-a-luck game is 5/36.
Example • An instructor states that the probability of passing the class, assuming that you pass the first test is 85%. • The probability that a bus will be in an accident on a specific run is about 6%.
• The probability of getting a royal flush when five cards are selected at random is 1/649,740. • The probability that a student will get a C or better in a statistics course is about 70%
• The probability that a new fast-food restaurant will be a success in Chicago is 35%. • The probability that interest rates will rise in the next 6 months is 0.50.
The Addition Rule for Probability • Two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common).
Example: Mutual Exclusiveness • Determine whether these events are mutually exclusive: • Roll a die and get an even number, and get a number less than 3 • Roll a die: Get a number greater than 3, and get a number less than 3
Example: Mutual Exclusiveness • Select a student in your college: The student is a sophomore, and the student is a business major. • Select a registered voter: The voter is a Republican and the voter is a Democrat.
Addition Rule 1. • When two events A and B are mutually exclusive, the probability that A or B will occur is • ______________________________
Example: • An automobile dealer has 10 Fords, 7 Buicks, and 5 Plymouths on her used car lot. If a person purchases a used car, find the probability that it is a Ford or a Buick?
Example: • One card is randomly selected from a standard 52-card deck. Find the probability that the selected card is an ace or a king.
Example: • An automobile dealership has found that 37 percent of its new car sales have been dealer financed, 45 percent have been financed by another institution, and 18 percent have been cash sales. Find the probability that the next purchase of a new car at this dealership will be either a cash sale or dealer financed.
Addition Rule 2 • If A and B are not mutually exclusive, then • ___________________________ • Note: This rule can also be used when A and B are mutually exclusive since P(A and B) will always equal 0 for mutually exclusive events.
Example • The probability that a student owns a car is 0.65, and the probability that a student owns a computer is 0.82. The probability that a student owns both is 0.55. • What is the probability that a given student owns a car or a computer?
Example: • The probability that a student owns a car is 0.65, and the probability that a student owns a computer is 0.82. The probability that a student owns both is 0.55. • What is the probability that a given student owns neither a car nor a computer?
Example • A single card is drawn from a deck. Find the probability of selecting • a four or a diamond
Example • A jack or a black card • a club or a diamond.
Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived 332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Example: Use the table below. Assume that one person aboard the Titanic is randomly selected. • Find the probability of selecting a woman or a girl.
Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived 332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Find the probability of selecting a woman or someone who survived.
Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived 332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Find the probability of selecting a woman or boy or girl.
Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived 332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Find the probability of selecting a woman or someone who died in the sinking of the ship.
Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived 332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Example: Use the table below. Assume that one person aboard the Titanic is randomly selected. • Find the probability of selecting a woman or a girl.
Example • At a used-book sale, 100 books are adult books and 160 are children’s books. Seventy of the adult books are nonfiction while 60 of the children’s books are nonfiction. If a book is selected at random, find the probability that it is • Fiction • not a children’s nonfiction • an adult book or a children’s nonfiction
4-4 The Multiplication Rules and Conditional Probability • Two events A and B are independent events if the fact that A occurs does not affect the probability of B occurring.
• Flipping a coin and getting heads • Flipping a coin a second time and getting heads • Speeding while driving to class • Getting a traffic ticket while driving to class • Finding that your car will not start • Finding that your kitchen light will not work
Multiplication Rule 1 • When two events are independent the probability of both occurring is ________________________
Example: • Find the probability of flipping a coin and getting tails and rolling a die and getting a 6.
Example: • One card is selected from a deck of 52 cards and replaced and then another card is selected. Find the probability of selecting a queen and then selecting a heart.
• Example: If 18% of all Americans are underweight, find the probability that if three Americans are selected at random, all will be underweight.
• The Multiplication Rule 1 can be extended to three or more independent events by using the formula • ______________________________
Example: • The Gallup Poll reported that 52% of Americans used a seat belt the last time they got into a car. If four people are selected at random, find the probability that they all used a seat belt the last time they got into a car.
• When the outcome or occurrence of the first event affects the outcome or occurrence of the second event in such a way that the probability is changed, the events are said to be dependent events.
Conditional Probability • The conditional probability of an event B in relationship to an event A is the probability that event B occurs after event A has already occurred. The notation for conditional probability is P(B|A).
Multiplication Rule 2 • When two events are dependent, the probability of both occurring is P(A and B) = P(A) * P(B|A)
Example: • If two cards are selected from a standard deck of 52 cards without replacement, find these probabilities. • Both are spades
Example: • If two cards are selected from a standard deck of 52 cards without replacement, find these probabilities. • Both are kings
Example: • If two cards are selected from a standard deck of 52 cards without replacement, find these probabilities. • Both are the same suit
Example • A flashlight has six batteries, two of which are defective. If two are selected at random without replacement, find the probability that both are defective.
Example • In a class containing twelve men and two women, 2 students are selected at random to given an impromptu speech. Find the probability that both are men.
Example: • An automobile manufacturer has three factories, A, B, and C. They produce 50%, 30%, and 20%, respectively of a specific model of car. Thirty percent of the cars produced in factory A are white, 40% of those produced in factory B are white, and 25% of those produced in factory C are white. If an automobile produced by the company is selected at random, find the probability that it is white.
Conditional Probability • Conditional Probability – Derived from formula for dependent events
• The probability that the second event B occurs given that the first event A has already occurred can be found by dividing the probability that both events occurred by the probability that the first event occurred. • The formula is __________________.
Example: • At a small college, the probability that a student takes physics and sociology is 0.092. The probability that a student takes sociology is 0.73. Find the probability that the student is taking physics, given that he or she is taking sociology.
Example • A circuit to run a model railroad has eight switches. Two are defective. If a person selects two switches at random and tests them, find the probability that the second one is defective, given that the first one is defective.
Example • In a pizza restaurant, 95% of the customers order pizza. If 65%of the customers order pizza and a salad, find the probability that a customer who orders pizza will also order a salad.
Example • The probability that it snows and the bus arrives late is 0.023. John hears the weather forecast, and there is a 40% chance of snow tomorrow. Find the probability that the bus will be late, given that it snows.
Example • Try at Home for Next Time Thirteen percent of the employees of a large company are female technicians. Forty percent of its workers are technicians. If a technician has been assigned to a particular job, what is the probability that the person is female?
• Example: The medal distribution from the 2000 Summer Olympic Games is shown in the table. Gold Silver Bronze United States 39 25 33 Russia 32 28 28 China 28 16 15 Australia 16 25 17 Others 186 205 235 • Find the probability that the winner won the gold medal, given that the winner was from the United States.
• Example: The medal distribution from the 2000 Summer Olympic Games is shown in the table. Gold Silver Bronze United States 39 25 33 Russia 32 28 28 China 28 16 15 Australia 16 25 17 Others 186 205 235 • Find the probability that the winner was from the United States, given that he or she won the gold medal.
Example: • Traffic entering an intersection can continue straight ahead or turn right. Eighty percent of the traffic flow is straight ahead. If a car continues straight, the probability of a collision is 0.0004; if a car turns right, the probability of a collision is 0.0036. Find the probability that a car entering the intersection will have a collision.
Example: • In situations where it is critical that a system function properly, additional backup systems are usually provided. Suppose a switch is used to activate a component in a satellite. If the switch fails, then a second switch takes over and activates the component. If each switch has a probability of 0.002 of failing, what is the probability that the component will be activated?
Example • A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a person is selected at random, find the probability that he or she will contract the disease.
At Least One • The complement of at least one is zero of the same type.
Example: • A game is played by drawing four cards from an ordinary deck and replacing each card after it is drawn. Find the probability of winning if at least one ace is drawn.
Example • A coin is tossed five times. Find the probability of getting at least one tail.
Example • It has been found that 40% of all people over the age of 85 suffer from Alzheimer’s disease. If three people over 85 are selected at random, find the probability that at least one person does not suffer from Alzheimer’s disease.
Example: • Among a class of 25 students, find the probability that at least two of them have the same birthday.
Example: • In a lab there are eight technicians. Three are male and five are female. If three technicians are selected, find the probability that at least one is female.
Example: • On a surprise quiz consisting of five truefalse questions, an unprepared student guesses each answer. Find the probability that he gets at least one correct.
Example: • A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medications, at least one person’s infection will not improve.
Fundamental Counting Rule • In a sequence of n events in which the first one has k possibilities and the second has k2 possibilities and the third has k3 possiblities and so fourth, the total number of possibilities of the sequence would be k1* k2 * k3. . . .
Example • There are eight different statistics books, 6 different geometry books and 3 different trigonometry books. A student must select one book of each type. How many different ways can this be done?
Example: • A college bookstore offers a personal computer system consisting of a computer, a monitor, and a printer. A student has a choice of two computers, three monitors, and two printers, all of which are compatible. In how many ways can a computer system be bundled?
• Factorial Formulas – For any counting number, n, • n! = _________________ • 0! = _________________
Factorial Rule • The arrangement of n objects is ________. (This is a special case of the permutation rule, where all n objects are being arranged.)
Example: • You are hosting a dinner party for eight people. In preparing the seating arrangement, you would like to know the number of different ways in which the guest can be arranged.
Example: • Five students are to give presentations in class on a particular day. In how many ways can the presentations be made?
Permutation • A permutation is an arrangement of n objects selected r at a time in a specific order.
Example • How many ordered seating arrangements can be made for eight people in five chairs?
• The board of directors of a local college has 12 members. Three officers—president, vicepresident and treasurer—must be elected from the members. How many different possible slates of officers are there?
Combination • A selection of distinct objects without regard to order is called a combination.
Combination Rule • The number of combinations of r objects selected from n objects is denoted by _________ and is given by the formula • ______________
Example: • How many different 5-card poker hands can be dealt from a standard deck of 52 cards?
Example: • A professor grades homework by randomly choosing 5 out of 12 homework problems to grade. How many different groups of problems can he possibly grade?
Example: • A sales representative must visit four cities: Omaha, Dallas, Wichita, and Oklahoma City. There are air connections between each of the cities. In how many orders can he visit the cities?
Example • A pizza shop offers a combination pizza consisting of a choice of any three of the four ingredients: pepperoni (P), mushrooms (M), sausage (S), and anchovies (A). Determine the number of possible combination pizzas.
Example • A professor grades homework by randomly choosing 5 out of 12 homework problems to grade. How many different groups of problems can he possibly grade?
Example: • There are three nursing positions to be filled at Lilly Hospital. Position one is the day nursing supervisor; position two is the night nursing supervisor; and position three is the nursing coordinator position. There are 15 candidates qualified for all three of the positions. In how many ways can the positions be filled by the applicants?
Example: • A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • All teachers
Example: • A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • 2 teachers and 2 parents
Example: • A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • All parents
Example: • A parent-teacher committee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • 1 teacher
Example: • An instructor gives her class a quiz that consists of 2 true/false questions, one multiple choice question with five selections, and 2 multiple choice questions with 4 choices each. One student did not prepare for the quiz and decides to randomly guess. In how many ways can the student fill out the quiz? • What’s the probability that the student gets a score of 100?
Example: • An instructor give her class a quiz that consists of 2 true/false questions, one multiple choice question with five selections, and 2 multiple choice questions with 4 choices each. One student did not prepare for the quiz and decides to randomly guess. In how many ways can the student fill out the quiz? • What’s the probability that the student gets a score of 80?
Example: • An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • All life policies
Example: • An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • Both homeowner’s policies
Example: • An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • All automobile policies
Example: • An insurance sales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • 1 of each policy.

More Related Content

PPT
probability
byUnsa Shakir
 
PPTX
introduction to probability
bylovemucheca
 
PPT
Basic Probability
bykaurab
 
PPTX
Sampling and sampling distributions
byStephan Jade Navarro
 
PPTX
Probability
byMayank Devnani
 
PPTX
law of large number and central limit theorem
bylovemucheca
 
PPTX
Probability distributions & expected values
byCollege of business administration
 
PDF
Basic concepts of probability
byAvjinder (Avi) Kaler
 
probability
byUnsa Shakir
 
introduction to probability
bylovemucheca
 
Basic Probability
bykaurab
 
Sampling and sampling distributions
byStephan Jade Navarro
 
Probability
byMayank Devnani
 
law of large number and central limit theorem
bylovemucheca
 
Probability distributions & expected values
byCollege of business administration
 
Basic concepts of probability
byAvjinder (Avi) Kaler
 

What's hot

PPT
Probability Concepts Applications
byguest44b78
 
PDF
Chapter 4 part3- Means and Variances of Random Variables
bynszakir
 
PDF
Simple linear regression
byAvjinder (Avi) Kaler
 
PPT
Basic concept of probability
byIkhlas Rahman
 
PDF
Chapter 5 part1- The Sampling Distribution of a Sample Mean
bynszakir
 
PPTX
Conditional probability
bysuncil0071
 
PPTX
Probability basics and bayes' theorem
byBalaji P
 
PPTX
Introduction to Statistics and Probability
byBhavana Singh
 
PPT
The sampling distribution
byHarve Abella
 
PPTX
Types of function
bySanaullahMemon10
 
PPTX
Counting
byLong Beach City College
 
PPT
Chapter 05
byTuul Tuul
 
PPTX
Compound interest
byWyeth Dalayap
 
PPTX
Conditional Probability
byMaria Romina Angustia
 
PPTX
Probability
byNaman Kumar
 
PPTX
Probability
bySanika Savdekar
 
PPT
Probability
byMaria Romina Angustia
 
PDF
Random Variable
byHabibullah Bahar University College
 
PPTX
Binomial probability distributions ppt
byTayab Ali
 
PDF
Nov. 4 Distance Between A Point And A Line
byRyanWatt
 
Probability Concepts Applications
byguest44b78
 
Chapter 4 part3- Means and Variances of Random Variables
bynszakir
 
Simple linear regression
byAvjinder (Avi) Kaler
 
Basic concept of probability
byIkhlas Rahman
 
Chapter 5 part1- The Sampling Distribution of a Sample Mean
bynszakir
 
Conditional probability
bysuncil0071
 
Probability basics and bayes' theorem
byBalaji P
 
Introduction to Statistics and Probability
byBhavana Singh
 
The sampling distribution
byHarve Abella
 
Types of function
bySanaullahMemon10
 
Counting
byLong Beach City College
 
Chapter 05
byTuul Tuul
 
Compound interest
byWyeth Dalayap
 
Conditional Probability
byMaria Romina Angustia
 
Probability
byNaman Kumar
 
Probability
bySanika Savdekar
 
Probability
byMaria Romina Angustia
 
Random Variable
byHabibullah Bahar University College
 
Binomial probability distributions ppt
byTayab Ali
 
Nov. 4 Distance Between A Point And A Line
byRyanWatt
 

Viewers also liked

PPT
Chapter 4
byRose Jenkins
 
PPT
Probability concept and Probability distribution
bySouthern Range, Berhampur, Odisha
 
PPTX
Sportsbetting tips-understanding probability
byMobile Betting
 
PPT
Forecasting Presentation
byjfhirsch
 
PPTX
Maneesh (economics)
byMadurai Kamaraj University
 
ODP
Philips Geometry Guide To Success.Ppt
byguest551837
 
PPTX
How angles add up!
byNCVPS
 
PDF
Pre-Cal 40S Slides May 27, 2008
byDarren Kuropatwa
 
PPT
004
byNing Ding
 
PPT
Les5e ppt 03
bySubas Nandy
 
PPTX
STAT: Probability (continuation)(2)
byTuenti SiIx
 
PPTX
Angle and shot guide (2)
byEmmaSlaterr
 
PPTX
1.7 angles and perpendicular lines
byHuron School District
 
ODP
Geometry Guide
byguestc5065b
 
PPT
Chapter 06
byTuul Tuul
 
PPT
Properties of triangles
byDreams4school
 
PPT
Geometry Guide
byguestac35d61
 
PPT
Statistik 1 6 distribusi probabilitas normal
bySelvin Hadi
 
PPT
Chapter 4 Probability Notes
bypwheeles
 
PPTX
The standard normal curve & its application in biomedical sciences
byAbhi Manu
 
Chapter 4
byRose Jenkins
 
Probability concept and Probability distribution
bySouthern Range, Berhampur, Odisha
 
Sportsbetting tips-understanding probability
byMobile Betting
 
Forecasting Presentation
byjfhirsch
 
Maneesh (economics)
byMadurai Kamaraj University
 
Philips Geometry Guide To Success.Ppt
byguest551837
 
How angles add up!
byNCVPS
 
Pre-Cal 40S Slides May 27, 2008
byDarren Kuropatwa
 
004
byNing Ding
 
Les5e ppt 03
bySubas Nandy
 
STAT: Probability (continuation)(2)
byTuenti SiIx
 
Angle and shot guide (2)
byEmmaSlaterr
 
1.7 angles and perpendicular lines
byHuron School District
 
Geometry Guide
byguestc5065b
 
Chapter 06
byTuul Tuul
 
Properties of triangles
byDreams4school
 
Geometry Guide
byguestac35d61
 
Statistik 1 6 distribusi probabilitas normal
bySelvin Hadi
 
Chapter 4 Probability Notes
bypwheeles
 
The standard normal curve & its application in biomedical sciences
byAbhi Manu
 

Similar to Chapter 4- probability

PPT
Chapter 4
byguest3720ca
 
PPTX
REVIEW OF BASIC PROBABILITY (1) (1).pptx
bymingyucao
 
PPTX
Cambridge IGCSE AS level Unit 4 - Probability.pptx
bymuhamed najeeb
 
PPT
Lesson 5.ppt
byOkianWarner
 
PPT
Chap005Lind.ppt
byManoloTaquire
 
PPT
Bab 5.ppt
byakhmadakbarsusamto1
 
PPTX
Addition rule and multiplication rule
byLong Beach City College
 
PDF
group1-151014013653-lva1-app6891.pdf
byVenkateshPandiri4
 
PPTX
Addition Rule and Multiplication Rule
byLong Beach City College
 
PPT
Chapter 05
bybmcfad01
 
PPT
PROBABILITY-MOD 2.ppt MBA study material
byliyaantony713
 
PPSX
Lecture on Statistics 1
bySHAYA'A OTHMAN MANAGEMENT & RESEARCH METHODOLOGY
 
PPT
Week 2 notes.ppt
byFaizanQadir10
 
PDF
Probability Concepts
byConflagratioNal Jahid
 
PPT
Chapter 4 260110 044531
byguest25d353
 
PPT
Basic Concepts of Probability_updated_Tm_31_5.ppt
byaymanrahman832835
 
PDF
probability-120904030152-phpapp01.pdf
byHimanshuSharma617324
 
PPT
Probability concepts and procedures law of profitability
bykamalsapkota13
 
PPT
Basic Concepts of Probability_updated_Tm_31_5_2.ppt
byMdFahimAbdullah22215
 
PPT
Probability addition rule
bylrassbach
 
Chapter 4
byguest3720ca
 
REVIEW OF BASIC PROBABILITY (1) (1).pptx
bymingyucao
 
Cambridge IGCSE AS level Unit 4 - Probability.pptx
bymuhamed najeeb
 
Lesson 5.ppt
byOkianWarner
 
Chap005Lind.ppt
byManoloTaquire
 
Bab 5.ppt
byakhmadakbarsusamto1
 
Addition rule and multiplication rule
byLong Beach City College
 
group1-151014013653-lva1-app6891.pdf
byVenkateshPandiri4
 
Addition Rule and Multiplication Rule
byLong Beach City College
 
Chapter 05
bybmcfad01
 
PROBABILITY-MOD 2.ppt MBA study material
byliyaantony713
 
Lecture on Statistics 1
bySHAYA'A OTHMAN MANAGEMENT & RESEARCH METHODOLOGY
 
Week 2 notes.ppt
byFaizanQadir10
 
Probability Concepts
byConflagratioNal Jahid
 
Chapter 4 260110 044531
byguest25d353
 
Basic Concepts of Probability_updated_Tm_31_5.ppt
byaymanrahman832835
 
probability-120904030152-phpapp01.pdf
byHimanshuSharma617324
 
Probability concepts and procedures law of profitability
bykamalsapkota13
 
Basic Concepts of Probability_updated_Tm_31_5_2.ppt
byMdFahimAbdullah22215
 
Probability addition rule
bylrassbach
 

Recently uploaded

PDF
Multicultural Strategy Playbook.pptx.pdf
byKathrynPeterson23
 
PDF
How LinkedIn Accounts Help Business Growth, Marketing & SEO
byJames Warne
 
PDF
From Stadiums to Smartphones: How Digital Marketing Is Redefining Fan Engagem...
bySushrutLondhe
 
DOCX
Just 5 Easy Steps to Buy a Verified Zelle Account.docx
bydmcmanusj
 
PDF
From stadiums to Screens Digital Marketing and the Future of Fan Engagement ...
byrautsrujal
 
PDF
2026 Digital Marketing Roadmap for Higher Education
byPhilippe Taza
 
PPTX
What is a Source Context in semantic seo?
bySemantic SEO BD
 
PDF
Facebook Group Marketing Tips for Sustainable Growth
byagrowth llc
 
DOCX
What Is Affiliate Influencer Marketing.docx
byWo Link
 
PDF
Google SERPs In 2026: Changes, Features & How To Boost Your Organic Traffic
bySearch Engine Journal
 
PDF
GitHub Accounts: Complete Guide for Developers, Businesses & Growth
byJames Warne
 
PPTX
The New Game Changer: How Interactive Advertising Is Transforming Sports Brands
bykarkiaditya17
 
PPTX
Google Local Services Ads Not Showing? 5 Fixes for Zero Impressions (LSA)
byDigital Harvest
 
PDF
Tommynguyne in vietnam ecosystem report modern marketing
byTommy Nguyen
 
PDF
Sell on Nykaa Fashion: A Visual Guide for New Brands & Sellers
byTouchstone Infotech
 
PDF
Facebook Event Marketing Tips for High-ROI Campaigns
byagrowth llc
 
PDF
Why Voice of Customer Is the Missing Layer in Positioning and Competitive Str...
byThe Digital Maze
 
PDF
The 2026 Sports Marketing Blueprint: Orchestrating Fan Engagement in India
bysubhamdollar
 
PDF
Webinar - Measuring & Winning AI Search Visibility | VertoDigital x Rankscale
byjules791567
 
PPTX
Increase Google LSA Impression Share: 5 Fixes to Spend More of Your Budget
byDigital Harvest
 
Multicultural Strategy Playbook.pptx.pdf
byKathrynPeterson23
 
How LinkedIn Accounts Help Business Growth, Marketing & SEO
byJames Warne
 
From Stadiums to Smartphones: How Digital Marketing Is Redefining Fan Engagem...
bySushrutLondhe
 
Just 5 Easy Steps to Buy a Verified Zelle Account.docx
bydmcmanusj
 
From stadiums to Screens Digital Marketing and the Future of Fan Engagement ...
byrautsrujal
 
2026 Digital Marketing Roadmap for Higher Education
byPhilippe Taza
 
What is a Source Context in semantic seo?
bySemantic SEO BD
 
Facebook Group Marketing Tips for Sustainable Growth
byagrowth llc
 
What Is Affiliate Influencer Marketing.docx
byWo Link
 
Google SERPs In 2026: Changes, Features & How To Boost Your Organic Traffic
bySearch Engine Journal
 
GitHub Accounts: Complete Guide for Developers, Businesses & Growth
byJames Warne
 
The New Game Changer: How Interactive Advertising Is Transforming Sports Brands
bykarkiaditya17
 
Google Local Services Ads Not Showing? 5 Fixes for Zero Impressions (LSA)
byDigital Harvest
 
Tommynguyne in vietnam ecosystem report modern marketing
byTommy Nguyen
 
Sell on Nykaa Fashion: A Visual Guide for New Brands & Sellers
byTouchstone Infotech
 
Facebook Event Marketing Tips for High-ROI Campaigns
byagrowth llc
 
Why Voice of Customer Is the Missing Layer in Positioning and Competitive Str...
byThe Digital Maze
 
The 2026 Sports Marketing Blueprint: Orchestrating Fan Engagement in India
bysubhamdollar
 
Webinar - Measuring & Winning AI Search Visibility | VertoDigital x Rankscale
byjules791567
 
Increase Google LSA Impression Share: 5 Fixes to Spend More of Your Budget
byDigital Harvest
 

Chapter 4- probability

  • 1.
  • 2.
    Probability • Probability isthe chance of an event occurring. • A probability experiment is a chance process that leads to well-defined results called outcomes. • An outcome is the result of a single trial of a probability experiment.
  • 3.
    • A samplespace is the set of all possible outcomes of a probability experiment.
  • 4.
    Example • Find thesample space for tossing two coins. • Find the sample space for tossing a coin and rolling a die.
  • 5.
    Example • Use atree diagram to determine the outcomes of an experiment of tossing three coins.
  • 6.
    • An eventis a set of outcomes. An event can be one outcome or more than one outcome. • An event with one outcome is called a simple event. • An event with more than one outcome is called a compound event.
  • 7.
    Example • The eventof drawing a card and getting a queen of hearts is a _____________ event. • The event of drawing a card and getting a spade is a ____________ event
  • 8.
    • Classical probabilityuses sample spaces to determine the numerical probability that an event will happen. • Classical probability assumes that all outcomes in the sample space are equally likely to occur.
  • 9.
    Formula for Classical Probability– • The probability of any event E is _________________________________ _____ = ________
  • 10.
    • Example: Ifa die is rolled one time, find these probabilities. a) of getting a 4 • b) of getting an even number • c) of getting a number greater than 4 • d) of getting a number greater than 3 and an odd number
  • 11.
    Probability Rules • Theprobability of an event E is a number between and including 0 and 1. 0 < P(E) < 1 • If an event E cannot occur, its probability is 0. • If an event E is certain to occur its probability is 1. • The sum of the probabilities of the outcomes in a sample space is 1.
  • 12.
    Complementary Events • Thecomplement of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by _______.
  • 13.
    Example • Find thecomplement of each event. • Flipping two coins and getting at least one head • Selecting a day of the week that has two syllables.
  • 14.
    Example • Find thecomplement of each event. – Rolling a die and getting a number greater than 4 – Drawing a card and getting a face card
  • 15.
    Rule for Complementary Events •_______________ • • • or __________________ or _______________
  • 16.
    Examples • An urncontains three red marbles, eight white marbles and 3 green marbles. Find the probability of selecting a marble that is not green. • Two dice are tossed. Find the probability of not getting doubles.
  • 17.
    Classical vs. Empirical Probability •The difference between classical and empirical probability is that classical probability assumes that certain outcomes are equally likely while empirical probability relies on actual observation to determine the likelihood of outcomes.
  • 18.
    Formula for Empirical Probability •Given a frequency distribution the probability of an event being in a given class is _____= ___________________________ =_______ • This probability is called empirical probability and is based on observation.
  • 19.
    Example: • The directorof the Readlot College Health Center wishes to open an eye clinic. To justify the expense of such a clinic, the director reports the probability that a student selected at random from the college roster needs corrective lenses. He took a random sample of 500 students to compute this probability and found that 375 of them need corrective lenses. What is the probability that a Readlot College student selected at random needs corrective lenses?
  • 20.
    Example • The Rightto Health Lobby wants to make a claim about the number of erroneous reports issued by a medical lab in one low-cost health center. Suppose they find in a random sample of 100 reports, 40 erroneous lab reports. What’s the probability that a report issued by this health center is erroneous?
  • 21.
    Law of LargeNumbers • As the number of trials increases the empirical probability will approach the theoretical probability.
  • 22.
    Subjective Probability • Subjectiveprobability uses a probability value based on an educated guess or estimate, employing opinions and inexact information.
  • 23.
    Example • Example: Classifyeach statement as an example of classical probability, empirical probability, or subjective probability. • The probability that a person will watch the 6:00 news. • The probability of winning at a chuck-a-luck game is 5/36.
  • 24.
    Example • An instructorstates that the probability of passing the class, assuming that you pass the first test is 85%. • The probability that a bus will be in an accident on a specific run is about 6%.
  • 25.
    • The probabilityof getting a royal flush when five cards are selected at random is 1/649,740. • The probability that a student will get a C or better in a statistics course is about 70%
  • 26.
    • The probabilitythat a new fast-food restaurant will be a success in Chicago is 35%. • The probability that interest rates will rise in the next 6 months is 0.50.
  • 27.
    The Addition Rulefor Probability • Two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common).
  • 28.
    Example: Mutual Exclusiveness • Determinewhether these events are mutually exclusive: • Roll a die and get an even number, and get a number less than 3 • Roll a die: Get a number greater than 3, and get a number less than 3
  • 29.
    Example: Mutual Exclusiveness • Selecta student in your college: The student is a sophomore, and the student is a business major. • Select a registered voter: The voter is a Republican and the voter is a Democrat.
  • 30.
    Addition Rule 1. •When two events A and B are mutually exclusive, the probability that A or B will occur is • ______________________________
  • 31.
    Example: • An automobiledealer has 10 Fords, 7 Buicks, and 5 Plymouths on her used car lot. If a person purchases a used car, find the probability that it is a Ford or a Buick?
  • 32.
    Example: • One cardis randomly selected from a standard 52-card deck. Find the probability that the selected card is an ace or a king.
  • 33.
    Example: • An automobiledealership has found that 37 percent of its new car sales have been dealer financed, 45 percent have been financed by another institution, and 18 percent have been cash sales. Find the probability that the next purchase of a new car at this dealership will be either a cash sale or dealer financed.
  • 34.
    Addition Rule 2 •If A and B are not mutually exclusive, then • ___________________________ • Note: This rule can also be used when A and B are mutually exclusive since P(A and B) will always equal 0 for mutually exclusive events.
  • 35.
    Example • The probabilitythat a student owns a car is 0.65, and the probability that a student owns a computer is 0.82. The probability that a student owns both is 0.55. • What is the probability that a given student owns a car or a computer?
  • 36.
    Example: • The probabilitythat a student owns a car is 0.65, and the probability that a student owns a computer is 0.82. The probability that a student owns both is 0.55. • What is the probability that a given student owns neither a car nor a computer?
  • 37.
    Example • A singlecard is drawn from a deck. Find the probability of selecting • a four or a diamond
  • 38.
    Example • A jackor a black card • a club or a diamond.
  • 39.
    Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Example: Use the table below. Assume that one person aboard the Titanic is randomly selected. • Find the probability of selecting a woman or a girl.
  • 40.
    Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Find the probability of selecting a woman or someone who survived.
  • 41.
    Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Find the probability of selecting a woman or boy or girl.
  • 42.
    Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Find the probability of selecting a woman or someone who died in the sinking of the ship.
  • 43.
    Example: Titanic Titanic Mortality Men Women Boys Girls Total Survived332 318 29 27 706 Died 104 35 18 1517 1360 Total 1692 422 64 45 2223 • Example: Use the table below. Assume that one person aboard the Titanic is randomly selected. • Find the probability of selecting a woman or a girl.
  • 44.
    Example • At aused-book sale, 100 books are adult books and 160 are children’s books. Seventy of the adult books are nonfiction while 60 of the children’s books are nonfiction. If a book is selected at random, find the probability that it is • Fiction • not a children’s nonfiction • an adult book or a children’s nonfiction
  • 45.
    4-4 The MultiplicationRules and Conditional Probability • Two events A and B are independent events if the fact that A occurs does not affect the probability of B occurring.
  • 46.
    • Flipping acoin and getting heads • Flipping a coin a second time and getting heads • Speeding while driving to class • Getting a traffic ticket while driving to class • Finding that your car will not start • Finding that your kitchen light will not work
  • 47.
    Multiplication Rule 1 •When two events are independent the probability of both occurring is ________________________
  • 48.
    Example: • Find theprobability of flipping a coin and getting tails and rolling a die and getting a 6.
  • 49.
    Example: • One cardis selected from a deck of 52 cards and replaced and then another card is selected. Find the probability of selecting a queen and then selecting a heart.
  • 50.
    • Example: If18% of all Americans are underweight, find the probability that if three Americans are selected at random, all will be underweight.
  • 51.
    • The MultiplicationRule 1 can be extended to three or more independent events by using the formula • ______________________________
  • 52.
    Example: • The GallupPoll reported that 52% of Americans used a seat belt the last time they got into a car. If four people are selected at random, find the probability that they all used a seat belt the last time they got into a car.
  • 53.
    • When theoutcome or occurrence of the first event affects the outcome or occurrence of the second event in such a way that the probability is changed, the events are said to be dependent events.
  • 54.
    Conditional Probability • Theconditional probability of an event B in relationship to an event A is the probability that event B occurs after event A has already occurred. The notation for conditional probability is P(B|A).
  • 55.
    Multiplication Rule 2 •When two events are dependent, the probability of both occurring is P(A and B) = P(A) * P(B|A)
  • 56.
    Example: • If twocards are selected from a standard deck of 52 cards without replacement, find these probabilities. • Both are spades
  • 57.
    Example: • If twocards are selected from a standard deck of 52 cards without replacement, find these probabilities. • Both are kings
  • 58.
    Example: • If twocards are selected from a standard deck of 52 cards without replacement, find these probabilities. • Both are the same suit
  • 59.
    Example • A flashlighthas six batteries, two of which are defective. If two are selected at random without replacement, find the probability that both are defective.
  • 60.
    Example • In aclass containing twelve men and two women, 2 students are selected at random to given an impromptu speech. Find the probability that both are men.
  • 61.
    Example: • An automobilemanufacturer has three factories, A, B, and C. They produce 50%, 30%, and 20%, respectively of a specific model of car. Thirty percent of the cars produced in factory A are white, 40% of those produced in factory B are white, and 25% of those produced in factory C are white. If an automobile produced by the company is selected at random, find the probability that it is white.
  • 62.
    Conditional Probability • ConditionalProbability – Derived from formula for dependent events
  • 63.
    • The probabilitythat the second event B occurs given that the first event A has already occurred can be found by dividing the probability that both events occurred by the probability that the first event occurred. • The formula is __________________.
  • 64.
    Example: • At asmall college, the probability that a student takes physics and sociology is 0.092. The probability that a student takes sociology is 0.73. Find the probability that the student is taking physics, given that he or she is taking sociology.
  • 65.
    Example • A circuitto run a model railroad has eight switches. Two are defective. If a person selects two switches at random and tests them, find the probability that the second one is defective, given that the first one is defective.
  • 66.
    Example • In apizza restaurant, 95% of the customers order pizza. If 65%of the customers order pizza and a salad, find the probability that a customer who orders pizza will also order a salad.
  • 67.
    Example • The probabilitythat it snows and the bus arrives late is 0.023. John hears the weather forecast, and there is a 40% chance of snow tomorrow. Find the probability that the bus will be late, given that it snows.
  • 68.
    Example • Try atHome for Next Time Thirteen percent of the employees of a large company are female technicians. Forty percent of its workers are technicians. If a technician has been assigned to a particular job, what is the probability that the person is female?
  • 69.
    • Example: Themedal distribution from the 2000 Summer Olympic Games is shown in the table. Gold Silver Bronze United States 39 25 33 Russia 32 28 28 China 28 16 15 Australia 16 25 17 Others 186 205 235 • Find the probability that the winner won the gold medal, given that the winner was from the United States.
  • 70.
    • Example: Themedal distribution from the 2000 Summer Olympic Games is shown in the table. Gold Silver Bronze United States 39 25 33 Russia 32 28 28 China 28 16 15 Australia 16 25 17 Others 186 205 235 • Find the probability that the winner was from the United States, given that he or she won the gold medal.
  • 71.
    Example: • Traffic enteringan intersection can continue straight ahead or turn right. Eighty percent of the traffic flow is straight ahead. If a car continues straight, the probability of a collision is 0.0004; if a car turns right, the probability of a collision is 0.0036. Find the probability that a car entering the intersection will have a collision.
  • 72.
    Example: • In situationswhere it is critical that a system function properly, additional backup systems are usually provided. Suppose a switch is used to activate a component in a satellite. If the switch fails, then a second switch takes over and activates the component. If each switch has a probability of 0.002 of failing, what is the probability that the component will be activated?
  • 73.
    Example • A vaccinehas a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a person is selected at random, find the probability that he or she will contract the disease.
  • 74.
    At Least One •The complement of at least one is zero of the same type.
  • 75.
    Example: • A gameis played by drawing four cards from an ordinary deck and replacing each card after it is drawn. Find the probability of winning if at least one ace is drawn.
  • 76.
    Example • A coinis tossed five times. Find the probability of getting at least one tail.
  • 77.
    Example • It hasbeen found that 40% of all people over the age of 85 suffer from Alzheimer’s disease. If three people over 85 are selected at random, find the probability that at least one person does not suffer from Alzheimer’s disease.
  • 78.
    Example: • Among aclass of 25 students, find the probability that at least two of them have the same birthday.
  • 79.
    Example: • In alab there are eight technicians. Three are male and five are female. If three technicians are selected, find the probability that at least one is female.
  • 80.
    Example: • On asurprise quiz consisting of five truefalse questions, an unprepared student guesses each answer. Find the probability that he gets at least one correct.
  • 81.
    Example: • A medicationis 75% effective against a bacterial infection. Find the probability that if 12 people take the medications, at least one person’s infection will not improve.
  • 82.
    Fundamental Counting Rule •In a sequence of n events in which the first one has k possibilities and the second has k2 possibilities and the third has k3 possiblities and so fourth, the total number of possibilities of the sequence would be k1* k2 * k3. . . .
  • 83.
    Example • There areeight different statistics books, 6 different geometry books and 3 different trigonometry books. A student must select one book of each type. How many different ways can this be done?
  • 84.
    Example: • A collegebookstore offers a personal computer system consisting of a computer, a monitor, and a printer. A student has a choice of two computers, three monitors, and two printers, all of which are compatible. In how many ways can a computer system be bundled?
  • 85.
    • Factorial Formulas– For any counting number, n, • n! = _________________ • 0! = _________________
  • 86.
    Factorial Rule • Thearrangement of n objects is ________. (This is a special case of the permutation rule, where all n objects are being arranged.)
  • 87.
    Example: • You arehosting a dinner party for eight people. In preparing the seating arrangement, you would like to know the number of different ways in which the guest can be arranged.
  • 88.
    Example: • Five studentsare to give presentations in class on a particular day. In how many ways can the presentations be made?
  • 89.
    Permutation • A permutationis an arrangement of n objects selected r at a time in a specific order.
  • 90.
    Example • How manyordered seating arrangements can be made for eight people in five chairs?
  • 91.
    • The boardof directors of a local college has 12 members. Three officers—president, vicepresident and treasurer—must be elected from the members. How many different possible slates of officers are there?
  • 92.
    Combination • A selectionof distinct objects without regard to order is called a combination.
  • 93.
    Combination Rule • Thenumber of combinations of r objects selected from n objects is denoted by _________ and is given by the formula • ______________
  • 94.
    Example: • How manydifferent 5-card poker hands can be dealt from a standard deck of 52 cards?
  • 95.
    Example: • A professorgrades homework by randomly choosing 5 out of 12 homework problems to grade. How many different groups of problems can he possibly grade?
  • 96.
    Example: • A salesrepresentative must visit four cities: Omaha, Dallas, Wichita, and Oklahoma City. There are air connections between each of the cities. In how many orders can he visit the cities?
  • 97.
    Example • A pizzashop offers a combination pizza consisting of a choice of any three of the four ingredients: pepperoni (P), mushrooms (M), sausage (S), and anchovies (A). Determine the number of possible combination pizzas.
  • 98.
    Example • A professorgrades homework by randomly choosing 5 out of 12 homework problems to grade. How many different groups of problems can he possibly grade?
  • 99.
    Example: • There arethree nursing positions to be filled at Lilly Hospital. Position one is the day nursing supervisor; position two is the night nursing supervisor; and position three is the nursing coordinator position. There are 15 candidates qualified for all three of the positions. In how many ways can the positions be filled by the applicants?
  • 100.
    Example: • A parent-teachercommittee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • All teachers
  • 101.
    Example: • A parent-teachercommittee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • 2 teachers and 2 parents
  • 102.
    Example: • A parent-teachercommittee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • All parents
  • 103.
    Example: • A parent-teachercommittee consisting of 4 people is to be formed from 20 parents and 5 teachers. Find the probability that the committee will consist of these people. (Assume that the selection will be random.) • 1 teacher
  • 104.
    Example: • An instructorgives her class a quiz that consists of 2 true/false questions, one multiple choice question with five selections, and 2 multiple choice questions with 4 choices each. One student did not prepare for the quiz and decides to randomly guess. In how many ways can the student fill out the quiz? • What’s the probability that the student gets a score of 100?
  • 105.
    Example: • An instructorgive her class a quiz that consists of 2 true/false questions, one multiple choice question with five selections, and 2 multiple choice questions with 4 choices each. One student did not prepare for the quiz and decides to randomly guess. In how many ways can the student fill out the quiz? • What’s the probability that the student gets a score of 80?
  • 106.
    Example: • An insurancesales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • All life policies
  • 107.
    Example: • An insurancesales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • Both homeowner’s policies
  • 108.
    Example: • An insurancesales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • All automobile policies
  • 109.
    Example: • An insurancesales representative selects three policies to review. The group of policies she can select from contains 8 life policies, 5 automobile polices, and 2 homeowner’s policies. Find the probability of selecting: • 1 of each policy.