1) The probability that exactly 10 out of 15 players use an MRF bat is 0.1859
2) The probability that more than 10 players use an MRF bat is 0.2173
3) The expected number of players using an MRF bat is 9
4) The variance of the number of players using an MRF bat is 3.6 and the standard deviation is 1.8974
The document defines key terms related to experimental probability such as experiment, outcome, and sample space. It provides examples of identifying the sample space and outcomes for experiments involving coin flips and rolling a die. The formula for calculating experimental probability is given as the number of times an event occurred divided by the total number of trials. An example is shown of a student calculating the probability of a coin landing on heads based on 30 coin flip trials.
The document discusses experimental probability and how it is calculated by performing trials of an experiment and recording the number of successful outcomes. It provides examples of calculating experimental probability based on rolling dice and cars moving in a race based on dice rolls. The document aims to help students understand what experimental probability means, become familiar with experimenting with chance, and compare experimental and actual probability.
This document provides information on probability distributions, including discrete and binomial distributions. It discusses the assumptions and characteristics of binomial distributions, using examples to show how they work. It also covers the Poisson distribution, its assumptions and function, and gives an example of calculating probabilities using the Poisson. The document ends with questions for practice with binomial and Poisson distributions.
Probability power point combo from holt ch 10lothomas
ย
This document covers probability concepts including experiments, outcomes, sample spaces, events, and probabilities. It defines key terms and provides examples of calculating probabilities of outcomes and events using concepts like the fundamental counting principle and determining if events are independent or dependent. Sample problems are given throughout for practicing these probability concepts and determining the number of possible outcomes, finding individual outcome probabilities, and calculating probabilities of compound events.
This document discusses various mathematical topics including probability, powers and exponents, and linear equations. It provides learning outcomes, examples, and outlines for each topic. Probability concepts covered include sample space, events, and calculating probability. Laws of exponents and using exponents to solve problems are explained for powers and exponents. Properties and solving techniques for linear equations are also outlined. An example shows how linear equations can be used to model and calculate economic order quantity to minimize inventory costs.
The document discusses binomial, Poisson, and hypergeometric probability distributions. It provides examples of experiments that follow each distribution and how to calculate probabilities using the respective formulas. For binomial experiments, the probability of success must be constant on each trial and trials must be independent. Poisson experiments involve rare, independent events with a known average rate. Hypergeometric probabilities are used when the probability of success changes on each dependent trial, such as sampling without replacement.
This presentation introduces probability and key concepts including:
- Calculating probability using the formula of favorable outcomes divided by total outcomes.
- Experimental and theoretical probabilities approaching each other as experiments increase (Law of Large Numbers).
- Basic probability rules including legitimate values between 0 and 1, sample space equals 1, addition, multiplication for independent events, and at least one event occurring.
- Examples are provided to demonstrate calculating probabilities of events including dependent vs independent events.
- Permutations and combinations are introduced to calculate arrangements and groupings of outcomes.
๏บPlease Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.2 - Binomial Probability Distributions
The document defines key terms related to experimental probability such as experiment, outcome, and sample space. It provides examples of identifying the sample space and outcomes for experiments involving coin flips and rolling a die. The formula for calculating experimental probability is given as the number of times an event occurred divided by the total number of trials. An example is shown of a student calculating the probability of a coin landing on heads based on 30 coin flip trials.
The document discusses experimental probability and how it is calculated by performing trials of an experiment and recording the number of successful outcomes. It provides examples of calculating experimental probability based on rolling dice and cars moving in a race based on dice rolls. The document aims to help students understand what experimental probability means, become familiar with experimenting with chance, and compare experimental and actual probability.
This document provides information on probability distributions, including discrete and binomial distributions. It discusses the assumptions and characteristics of binomial distributions, using examples to show how they work. It also covers the Poisson distribution, its assumptions and function, and gives an example of calculating probabilities using the Poisson. The document ends with questions for practice with binomial and Poisson distributions.
Probability power point combo from holt ch 10lothomas
ย
This document covers probability concepts including experiments, outcomes, sample spaces, events, and probabilities. It defines key terms and provides examples of calculating probabilities of outcomes and events using concepts like the fundamental counting principle and determining if events are independent or dependent. Sample problems are given throughout for practicing these probability concepts and determining the number of possible outcomes, finding individual outcome probabilities, and calculating probabilities of compound events.
This document discusses various mathematical topics including probability, powers and exponents, and linear equations. It provides learning outcomes, examples, and outlines for each topic. Probability concepts covered include sample space, events, and calculating probability. Laws of exponents and using exponents to solve problems are explained for powers and exponents. Properties and solving techniques for linear equations are also outlined. An example shows how linear equations can be used to model and calculate economic order quantity to minimize inventory costs.
The document discusses binomial, Poisson, and hypergeometric probability distributions. It provides examples of experiments that follow each distribution and how to calculate probabilities using the respective formulas. For binomial experiments, the probability of success must be constant on each trial and trials must be independent. Poisson experiments involve rare, independent events with a known average rate. Hypergeometric probabilities are used when the probability of success changes on each dependent trial, such as sampling without replacement.
This presentation introduces probability and key concepts including:
- Calculating probability using the formula of favorable outcomes divided by total outcomes.
- Experimental and theoretical probabilities approaching each other as experiments increase (Law of Large Numbers).
- Basic probability rules including legitimate values between 0 and 1, sample space equals 1, addition, multiplication for independent events, and at least one event occurring.
- Examples are provided to demonstrate calculating probabilities of events including dependent vs independent events.
- Permutations and combinations are introduced to calculate arrangements and groupings of outcomes.
๏บPlease Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 5: Discrete Probability Distribution
5.2 - Binomial Probability Distributions
This document provides information about the binomial probability distribution, including its basics and terminology. A binomial experiment has n repeated trials with two possible outcomes (success/failure), where the probability of success p remains constant from trial to trial. The number of successes X in n trials is a binomial random variable with a binomial probability distribution given by the formula P(X)=Cn*px*q^n-x, where q is the probability of failure. Several examples demonstrate calculating probabilities of outcomes for binomial experiments.
binomial probability distribution for statistics andd mangement mba notesSoujanyaLk1
ย
This document provides information about the binomial probability distribution, including its basics and terminology. A binomial experiment has n repeated trials with two possible outcomes (success/failure), where the probability of success p remains constant from trial to trial. The number of successes X in n trials is a binomial random variable with a binomial probability distribution given by the formula P(X)=Cn*px*q^n-x. Several examples demonstrate calculating probabilities of outcomes for binomial experiments with given values of n, p, and X.
The document provides a review of topics covered in a statistics course for a final exam. It includes sample problems related to regression analysis, correlation, probability distributions, hypothesis testing, and descriptive statistics. Students are asked to calculate predictions, interpret correlation coefficients, find probabilities using the binomial and Poisson distributions, determine sample sizes, and interpret hypothesis tests, among other tasks.
This document provides information about binomial and Poisson distributions. It includes examples of calculating probabilities for binomial distributions using the binomial probability formula and binomial tables. It also provides the key characteristics and formula for the Poisson distribution. The mean, variance and standard deviation are defined for binomial distributions. Examples are provided to demonstrate calculating these values.
This document provides an overview of experimental probability:
- It defines key terms like experiment, trial, outcome, and sample space.
- It explains how to calculate experimental probability by taking the number of times an event occurs over the total number of trials.
- It discusses how experimental probability can be used to make predictions about future experiments based on past results.
This document provides examples and explanations of key concepts in probability, including:
1) Probability is a number between 0 and 1 that indicates the likelihood of an event. Experimental probability is calculated from observations, while theoretical probability uses the composition of a sample space.
2) Tree diagrams and the fundamental counting principle can be used to determine the number of possible outcomes and probabilities in multi-stage experiments.
3) Union, intersection, and complements of events are probability concepts used to calculate probabilities of combined events.
This document is a lesson on experimental probability from Holt Algebra 1. It begins with examples of writing fractions, decimals, and percents. Then it defines key terms like experiment, trial, outcome, sample space, and event. Examples are given to identify sample spaces and outcomes. The likelihood of events is described using terms like impossible, unlikely, likely, and certain. Experimental probability is defined as the ratio of times an event occurs to the total number of trials. Examples show how to calculate experimental probability from outcome frequencies. The lesson ends with examples of using experimental probability to make predictions.
The document discusses the concept of probability, including defining it as a measure of likelihood between 0 and 1, and how to calculate probabilities using concepts like sample spaces, favorable outcomes, and total possible outcomes. It provides examples of calculating probabilities from experiments involving dice, cards, and coins. The document also outlines some applications of probability theory in areas like risk assessment, commodity markets, product reliability, and environmental regulation.
Here are the probabilities of the compound events in the assignment:
1a) The probability of drawing an 8 or 16 is 2/20 = 0.1
1b) The probability of drawing a 5 or a number divisible by 3 is 11/20
1c) The probability of drawing an odd number or a number divisible by 3 is 17/20
1d) The probability of drawing a number divisible by 3 or divisible by 4 is 19/20
2) The probability of drawing a violet marble or a pink marble is 40/52
3) The probability that a randomly selected household has a rabbit or a dog is 1824/4820 + 720/4820 - 252/48
This document provides teaching materials on multiplication for grade 2 students. It includes the competencies, indicators, examples and explanations of multiplication as repeated addition, and properties like the commutative and associative properties. It also contains practice problems for students involving word problems with multiplication. The goal is for students to understand multiplication concepts and be able to solve problems with numbers up to two digits.
This presentation provides an introduction to basic probability concepts. It defines probability as the study of randomness and uncertainty, and describes how probability was originally associated with games of chance. Key concepts discussed include random experiments, sample spaces, events, unions and intersections of events, and Venn diagrams. The presentation establishes the axioms of probability, including that a probability must be between 0 and 1, the probability of the sample space is 1, and probabilities of mutually exclusive events sum to the total probability. Formulas for computing probabilities of unions, intersections, and complements of events are also presented.
Topic Covered in this video:
1. What is Discrete Probability Distribution
2. Types of Theoretical Discrete Probability Distribution
3. Binomial Distribution
4. Properties of Binomial Distribution
5. Examples of Binomial distribution
6. Fitting of Binomial Distribution
7. Application of Binomial distribution
This document discusses experimental probability and how to calculate it. It provides examples of finding the probability of events occurring based on trial results. Experimental probability can be used to make predictions about future trials. Students are asked to identify sample spaces, outcomes, and probabilities in examples and quiz questions to practice these concepts.
1. The document contains a mathematics exam paper with 22 multiple-choice and word problems.
2. It provides instructions for candidates to write their answers in the spaces provided and show all working.
3. The exam covers a range of mathematics topics including algebra, geometry, statistics, and trigonometry.
Some Basic concepts of Probability along with advanced concepts on Medical probability & Probability in Gambling. A lot of Sample Questions and Practice Questions will help you understand and apply the concepts in real life.
Okay, here are the steps to convert each score to a z-score:
For history test:
Z = (X - Mean) / Standard Deviation
Z = (78 - 79) / 6
Z = -0.167
For math test:
Z = (X - Mean) / Standard Deviation
Z = (82 - 84) / 5
Z = 0.8
So the z-score for the history test is -0.167 and the z-score for the math test is 0.8.
This document discusses permutations and combinations. It defines permutations as arrangements that consider order, and combinations as arrangements where order does not matter. The document provides examples of using formulas and the fundamental counting principle to calculate the number of permutations and combinations in different scenarios, such as selecting committees from a group of people or hands of cards from a deck. It emphasizes that there are always fewer combinations than permutations since combinations ignore order.
Rounding and approximation are covered, including:
- Rounding numbers to a given number of decimal places or significant figures.
- Approximating multiplication and division calculations by rounding each number to 1 significant figure first.
- Examples of rounding numbers in different contexts are provided and the importance of checking the required level of accuracy is emphasized.
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
ย
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
This document provides information about the binomial probability distribution, including its basics and terminology. A binomial experiment has n repeated trials with two possible outcomes (success/failure), where the probability of success p remains constant from trial to trial. The number of successes X in n trials is a binomial random variable with a binomial probability distribution given by the formula P(X)=Cn*px*q^n-x, where q is the probability of failure. Several examples demonstrate calculating probabilities of outcomes for binomial experiments.
binomial probability distribution for statistics andd mangement mba notesSoujanyaLk1
ย
This document provides information about the binomial probability distribution, including its basics and terminology. A binomial experiment has n repeated trials with two possible outcomes (success/failure), where the probability of success p remains constant from trial to trial. The number of successes X in n trials is a binomial random variable with a binomial probability distribution given by the formula P(X)=Cn*px*q^n-x. Several examples demonstrate calculating probabilities of outcomes for binomial experiments with given values of n, p, and X.
The document provides a review of topics covered in a statistics course for a final exam. It includes sample problems related to regression analysis, correlation, probability distributions, hypothesis testing, and descriptive statistics. Students are asked to calculate predictions, interpret correlation coefficients, find probabilities using the binomial and Poisson distributions, determine sample sizes, and interpret hypothesis tests, among other tasks.
This document provides information about binomial and Poisson distributions. It includes examples of calculating probabilities for binomial distributions using the binomial probability formula and binomial tables. It also provides the key characteristics and formula for the Poisson distribution. The mean, variance and standard deviation are defined for binomial distributions. Examples are provided to demonstrate calculating these values.
This document provides an overview of experimental probability:
- It defines key terms like experiment, trial, outcome, and sample space.
- It explains how to calculate experimental probability by taking the number of times an event occurs over the total number of trials.
- It discusses how experimental probability can be used to make predictions about future experiments based on past results.
This document provides examples and explanations of key concepts in probability, including:
1) Probability is a number between 0 and 1 that indicates the likelihood of an event. Experimental probability is calculated from observations, while theoretical probability uses the composition of a sample space.
2) Tree diagrams and the fundamental counting principle can be used to determine the number of possible outcomes and probabilities in multi-stage experiments.
3) Union, intersection, and complements of events are probability concepts used to calculate probabilities of combined events.
This document is a lesson on experimental probability from Holt Algebra 1. It begins with examples of writing fractions, decimals, and percents. Then it defines key terms like experiment, trial, outcome, sample space, and event. Examples are given to identify sample spaces and outcomes. The likelihood of events is described using terms like impossible, unlikely, likely, and certain. Experimental probability is defined as the ratio of times an event occurs to the total number of trials. Examples show how to calculate experimental probability from outcome frequencies. The lesson ends with examples of using experimental probability to make predictions.
The document discusses the concept of probability, including defining it as a measure of likelihood between 0 and 1, and how to calculate probabilities using concepts like sample spaces, favorable outcomes, and total possible outcomes. It provides examples of calculating probabilities from experiments involving dice, cards, and coins. The document also outlines some applications of probability theory in areas like risk assessment, commodity markets, product reliability, and environmental regulation.
Here are the probabilities of the compound events in the assignment:
1a) The probability of drawing an 8 or 16 is 2/20 = 0.1
1b) The probability of drawing a 5 or a number divisible by 3 is 11/20
1c) The probability of drawing an odd number or a number divisible by 3 is 17/20
1d) The probability of drawing a number divisible by 3 or divisible by 4 is 19/20
2) The probability of drawing a violet marble or a pink marble is 40/52
3) The probability that a randomly selected household has a rabbit or a dog is 1824/4820 + 720/4820 - 252/48
This document provides teaching materials on multiplication for grade 2 students. It includes the competencies, indicators, examples and explanations of multiplication as repeated addition, and properties like the commutative and associative properties. It also contains practice problems for students involving word problems with multiplication. The goal is for students to understand multiplication concepts and be able to solve problems with numbers up to two digits.
This presentation provides an introduction to basic probability concepts. It defines probability as the study of randomness and uncertainty, and describes how probability was originally associated with games of chance. Key concepts discussed include random experiments, sample spaces, events, unions and intersections of events, and Venn diagrams. The presentation establishes the axioms of probability, including that a probability must be between 0 and 1, the probability of the sample space is 1, and probabilities of mutually exclusive events sum to the total probability. Formulas for computing probabilities of unions, intersections, and complements of events are also presented.
Topic Covered in this video:
1. What is Discrete Probability Distribution
2. Types of Theoretical Discrete Probability Distribution
3. Binomial Distribution
4. Properties of Binomial Distribution
5. Examples of Binomial distribution
6. Fitting of Binomial Distribution
7. Application of Binomial distribution
This document discusses experimental probability and how to calculate it. It provides examples of finding the probability of events occurring based on trial results. Experimental probability can be used to make predictions about future trials. Students are asked to identify sample spaces, outcomes, and probabilities in examples and quiz questions to practice these concepts.
1. The document contains a mathematics exam paper with 22 multiple-choice and word problems.
2. It provides instructions for candidates to write their answers in the spaces provided and show all working.
3. The exam covers a range of mathematics topics including algebra, geometry, statistics, and trigonometry.
Some Basic concepts of Probability along with advanced concepts on Medical probability & Probability in Gambling. A lot of Sample Questions and Practice Questions will help you understand and apply the concepts in real life.
Okay, here are the steps to convert each score to a z-score:
For history test:
Z = (X - Mean) / Standard Deviation
Z = (78 - 79) / 6
Z = -0.167
For math test:
Z = (X - Mean) / Standard Deviation
Z = (82 - 84) / 5
Z = 0.8
So the z-score for the history test is -0.167 and the z-score for the math test is 0.8.
This document discusses permutations and combinations. It defines permutations as arrangements that consider order, and combinations as arrangements where order does not matter. The document provides examples of using formulas and the fundamental counting principle to calculate the number of permutations and combinations in different scenarios, such as selecting committees from a group of people or hands of cards from a deck. It emphasizes that there are always fewer combinations than permutations since combinations ignore order.
Rounding and approximation are covered, including:
- Rounding numbers to a given number of decimal places or significant figures.
- Approximating multiplication and division calculations by rounding each number to 1 significant figure first.
- Examples of rounding numbers in different contexts are provided and the importance of checking the required level of accuracy is emphasized.
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
ย
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
ย
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
How Barcodes Can Be Leveraged Within Odoo 17Celine George
ย
In this presentation, we will explore how barcodes can be leveraged within Odoo 17 to streamline our manufacturing processes. We will cover the configuration steps, how to utilize barcodes in different manufacturing scenarios, and the overall benefits of implementing this technology.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
ย
(๐๐๐ ๐๐๐) (๐๐๐ฌ๐ฌ๐จ๐ง ๐)-๐๐ซ๐๐ฅ๐ข๐ฆ๐ฌ
๐๐ข๐ฌ๐๐ฎ๐ฌ๐ฌ ๐ญ๐ก๐ ๐๐๐ ๐๐ฎ๐ซ๐ซ๐ข๐๐ฎ๐ฅ๐ฎ๐ฆ ๐ข๐ง ๐ญ๐ก๐ ๐๐ก๐ข๐ฅ๐ข๐ฉ๐ฉ๐ข๐ง๐๐ฌ:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
๐๐ฑ๐ฉ๐ฅ๐๐ข๐ง ๐ญ๐ก๐ ๐๐๐ญ๐ฎ๐ซ๐ ๐๐ง๐ ๐๐๐จ๐ฉ๐ ๐จ๐ ๐๐ง ๐๐ง๐ญ๐ซ๐๐ฉ๐ซ๐๐ง๐๐ฎ๐ซ:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
ย
Ivรกn Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
BรI TแบฌP Bแป TRแปข TIแบพNG ANH LแปP 9 Cแบข NฤM - GLOBAL SUCCESS - NฤM HแปC 2024-2025 - ...
ย
Binomial distribution
1. Binomial Probability Distributions
A coin-tossing experiment is a simple example of an
important discrete random variable called the binomial
random variable.
Example- A sociologist is interested in the proportion of
elementary school teachers who are men or women
Example- A soft-drink marketer is interested in the
proportion of drinkers who prefer the brand or not
2. Example- A sales person interested in sale of a policy, if
he visits 10 people in a day what is the probability of
his selling policy to one person, or 2 person, โฆ.
Example- If ten persons enter the shop, what is the
probability that he will purchase the Mobile, or 2 will
purchase the mobile and so on
3. Definition: A binomial experiment is one that has these
four characteristics:
1. The experiment consists of n identical results/
trials/ observation.
2. Each trial results in one of two outcomes: one
outcome is called a success, S, and the other a failure,
F.
3. The probability of success on a single trial is equal
to p and remains the same from trial to trial. The
probability of failure is equal to (1 - p) = q.
4. The trials are independent.
4. The Binomial Probability function
( )!
( ) (1 )
!( )!
x n xn
f x p p
x n x
-
= -
-
x = the number of successes
p = the probability of a success on one trial
n = the number of trials
f(x) = the probability of x successes in n trials
5. Mean and Standard Deviation for the Binomial
Random Variable:
Mean: m = np
Variance: s 2 = npq
Standard deviation: npq=s
6. Binomial Formula. Suppose a binomial
experiment consists of n trials and results
in x successes. If the probability of success on
an individual trial is P, then the binomial
probability is:
b(x; n, P) = nCx * Px * (1 - P)n โ x
b(x; n, P) = nCr * Pr * (1 - P)n โ r
Where r is the value which the random variable takes
7. EXAMPLE
Suppose a coin is tossed 2 times. What is the probability of getting
(a) 0 head
Solution: This is a binomial experiment in which the number of trials is
equal to 2, the number of successes is equal to 0, and the probability
of success on a single trial is 1/2. Therefore, the binomial probability
is:
b(0; 2, 0.5) = 2C0 * (0.5)0 * (0.5)2
= 1/4
(b) 1 head
b(1; 2, 0.5) = 2C1 * (0.5)1 * (0.5)1
= 2/4
(c) 2 head
b(2; 2, 0.5) = 2C2 * (0.5)2 * (0.5)0
= 1/4
8. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(a) 0 head
Solution: This is a binomial experiment in which the number of trials is
equal to 10, the number of successes is equal to 0, and the
probability of success on a single trial is 1/2. Therefore, the binomial
probability is:
b(0; 10, 0.5) = 10C0 * (0.5)0 * (0.5)10
= 1/1024
Number of
Trial
1 2 3 4 5 6 7 8 9 10
outcome T T T T T T T T T T
Probability 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
9. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(b) 1 head
Number of
Trial
1 2 3 4 5 6 7 8 9 10
Outcome 1 H T T T T T T T T T
10. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(b) 1 head
Number of
Trial
1 2 3 4 5 6 7 8 9 10
Outcome 1 H T T T T T T T T T
Outcome 2 T H T T T T T T T T
11. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(b) 1 head
Number of
Trial
1 2 3 4 5 6 7 8 9 10
Outcome 1 H T T T T T T T T T
Outcome 2 T H T T T T T T T T
Outcome 3 T T H T T T T T T T
12. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(b) 1 head
Number of
Trial
1 2 3 4 5 6 7 8 9 10
Outcome 1 H T T T T T T T T T
Outcome 2 T H T T T T T T T T
Outcome 3 T T H T T T T T T T
Outcome 4 T T T H T T T T T T
13. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(b) 1 head
Number of
Trial
1 2 3 4 5 6 7 8 9 10
Outcome 1 H T T T T T T T T T
Outcome 2 T H T T T T T T T T
Outcome 3 T T H T T T T T T T
Outcome 4 T T T H T T T T T T
Outcome 5 T T T T H T T T T T
Outcome 6 T T T T T H T T T T
Outcome 7 T T T T T T H T T T
Outcome 8 T T T T T T T H T T
Outcome 9 T T T T T T T T H T
Outcome 10 T T T T T T T T T H
14. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(b) 1 head
Number of
Trial
1 2 3 4 5 6 7 8 9 10
Outcome 1 H T T T T T T T T T
Outcome 2 T H T T T T T T T T
Outcome 3 T T H T T T T T T T
Outcome 4 T T T H T T T T T T
Outcome 5 T T T T H T T T T T
Outcome 6 T T T T T H T T T T
Outcome 7 T T T T T T H T T T
Outcome 8 T T T T T T T H T T
Outcome 9 T T T T T T T T H T
Outcome 10 T T T T T T T T T H
Probability 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
15. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(b) 1 head
b(1; 10, 0.5) =
10C1 * (0.5)1 * (0.5)9
= 10/1024
16. EXAMPLE
Suppose a coin is tossed 10 times. What is the probability of getting
(c) 2 head
b(2; 10, 0.5) = 10C2 * (0.5)2 * (0.5)8
= 45/1024
17. As a Sales Manager you analyze the sales
records for all sales persons under your
guidance.
Ram has a success rate of 75% and average
10 sales calls per day. Shyam has a success
rate of 45% but average 16 calls per day
What is the probability that each sales
person makes 6 sales on any given day
18. A manufacturer is making a
product with a 20% defective rate.
if we select 5 randomly chosen
items at the end of the assembly
line, what is the probability of
having 1 defective items in our
sample?
19. EXAMPLE-
Suppose you take a multiple choice test with
10 questions, and each question has five
answer choices, what is the probability you
get exactly 4 questions correct just by
guessing
Number of trails= n= 10, event is correct
answer, P(Success)=1/5
Interested in 4 correct answers, r= 4
20. In San Francisco, 30% of workers take public transportation daily
1. In a sample of 10 workers, what is the probability that exactly
three workers take public transportation daily
2. In a sample of 10 workers, what is the probability that at least
three workers take public transportation daily
3. How many workers are expected to take public transportation
daily?
4. Compute the variance of the number of workers that will take the
public transport daily.
5. Compute the standard deviation of the number of workers that
will take the public transportation daily.
21. In San Francisco, 30% of workers take public transportation daily
1. In a sample of 10 workers, what is the probability that exactly
three workers take public transportation daily= 0.2668
2. In a sample of 10 workers, what is the probability that at least
three workers take public transportation daily= 0.6172
3. How many workers are expected to take public transportation
daily? = 3
4. Compute the variance of the number of workers that will take the
public transport daily. = 2.10
5. Compute the standard deviation of the number of workers that
will take the public transportation daily.= 1.449
22. Twelve of the top twenty finishers in the 2009 PGA Championship at
Hazeltine National Golf Club in Chaska, Minnesota, used a Titleist
brand golf ball (Golf Ball Test website, November 12, 2009). Suppose
these results are representative of the probability that a randomly
selected PGA Tour player uses a Titleist brand golf ball. For a sample of
15 PGA Tour players, make the following calculation
Compute the probability that exactly 10 of the 15 PGA Tour players use
a Titleist brand golf ball
Compute the probability that more than 10 of the 15 PGA Tour players
use a Titleist brand golf ball
For a sample of 15 PGA Tour players, compute the expected number of
players who use a Titleist brand golf ball
For a sample of 15 PGA Tour players, compute the variance and
standard deviation of the number of players who use a Titleist brand
golf ball
23. Using the 20 golfers in the Hazeltine PGA Championship, the
probability that a PGA professional golfer uses a Titleist brand golf ball
is p = 14/20 = .6
For the sample of 15 PGA Tour players, use a binomial distribution with
n = 15 and p = .6
F(10)= 0.1859
P(x > 10) = f (11) + f (12) + f (13) + f (14) + f (15)
.1268 + .0634 + .0219 + .0047 + .0005 = .2173
E(x) = np = 15(.6) = 9
Var(x) = s2 = np(1 - p) = 15(.6)(1 - .6) = 3.6
SD= 1.8974
24. A brokerage survey reports that 30 percent of
individual investors have used a discount broker (i.e
one which does not charge the full commission). In a
random sample of 10 individuals, what is the
probability that
a. Exactly two of the sampled individuals have used a
discount broker
b. Not more than three have used a discount broker
c. At least three of them have used a discount broker.
25. Example-
12 out of 20 players in IPL used MRF Bat and won the match. For a
randomly selected sample of 20 such players of IPL. Find the
probability that
1. exactly 10 out of 15 players use MRF bat.
2. More then 10 players use MRF bat
3. Find the expected number of players using MRF bat
4. Find the SD and variance of the number of players using MRF bat