TYPES OF EVENTS.pdf
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The document discusses different types of probability events: - Sure events have a probability of 1 and will always occur. Impossible events have a probability of 0. - Complementary events cover all possible outcomes such that one event must occur. - Mutually exclusive events cannot occur together, while mutually inclusive events can occur simultaneously. - Exhaustive events together cover all possible outcomes such that one is sure to occur. Equally likely events have outcomes that are equally possible. - An example calculates the probability of randomly selecting a number greater than 13 from numbers 1 to 25. The probability is 12/25.
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Basic concept of probability
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.
Probability
History behind the
development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
Basic Things About The Concept
Probability is used to quantify an attitude of mind towards some uncertainย proposition.
The higher the probability of an event, the more certain we are that the event will occur.ย
probability
1. Probability is the study of randomness and uncertainty of outcomes from experiments or processes. It allows us to make statements about the likelihood of events occurring.
2. Events are outcomes or sets of outcomes from random experiments. The probability of an event is calculated based on the number of outcomes in the event compared to the total number of possible outcomes.
3. Conditional probability is the likelihood of one event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. Conditional probabilities are useful for problems involving dependent events.
Probability
This document defines key concepts in probability and provides examples. It discusses probability vocabulary like sample space, outcome, trial, and event. It defines probability as the number of times a desired outcome occurs over total trials. Events are independent if the outcome of one does not impact others, and mutually exclusive if they cannot occur together. The addition and multiplication rules for probability are explained. Conditional probability describes the probability of a second event depending on the first occurring. Counting techniques are discussed for finding total possible outcomes of combined experiments. Review questions are provided to test understanding of the material.
Probability
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.
Random variable,Discrete and Continuous
Random variables can be either discrete or continuous. A discrete random variable takes on countable values, while a continuous random variable can take on any value within a range. The probability distributions for discrete and continuous random variables are different. A discrete probability distribution lists each possible value and its probability, while a continuous distribution is described using a probability density function. Random variables are used widely in statistics and probability to model outcomes of experiments and random phenomena.
Probability
This document defines key terminology related to probability, including:
- Sample space: The set of all possible outcomes of a random experiment.
- Events: One or more possible outcomes of an experiment.
- Equally likely events: Events with an equal chance of occurring.
- Mutually exclusive events: Events that cannot occur together.
- Exhaustive events: A set of events where one of the events must occur.
It also provides examples and introduces the classical definition of probability as the number of favorable outcomes divided by the total number of outcomes.
4.1-4.2 Sample Spaces and Probability
The document defines key concepts in probability theory, such as probability experiments, outcomes, sample spaces, events, classical probability, empirical probability, and subjective probability. It provides examples of how to calculate probabilities of simple and compound events using classical probability methods, including determining probabilities using fractions or decimals and interpreting "and" and "or" probabilities.
Recommended
Basic concept of probability
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.
Probability
History behind the
development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
Basic Things About The Concept
Probability is used to quantify an attitude of mind towards some uncertainย proposition.
The higher the probability of an event, the more certain we are that the event will occur.ย
probability
1. Probability is the study of randomness and uncertainty of outcomes from experiments or processes. It allows us to make statements about the likelihood of events occurring.
2. Events are outcomes or sets of outcomes from random experiments. The probability of an event is calculated based on the number of outcomes in the event compared to the total number of possible outcomes.
3. Conditional probability is the likelihood of one event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. Conditional probabilities are useful for problems involving dependent events.
Probability
This document defines key concepts in probability and provides examples. It discusses probability vocabulary like sample space, outcome, trial, and event. It defines probability as the number of times a desired outcome occurs over total trials. Events are independent if the outcome of one does not impact others, and mutually exclusive if they cannot occur together. The addition and multiplication rules for probability are explained. Conditional probability describes the probability of a second event depending on the first occurring. Counting techniques are discussed for finding total possible outcomes of combined experiments. Review questions are provided to test understanding of the material.
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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.
Random variable,Discrete and Continuous
Random variables can be either discrete or continuous. A discrete random variable takes on countable values, while a continuous random variable can take on any value within a range. The probability distributions for discrete and continuous random variables are different. A discrete probability distribution lists each possible value and its probability, while a continuous distribution is described using a probability density function. Random variables are used widely in statistics and probability to model outcomes of experiments and random phenomena.
Probability
This document defines key terminology related to probability, including:
- Sample space: The set of all possible outcomes of a random experiment.
- Events: One or more possible outcomes of an experiment.
- Equally likely events: Events with an equal chance of occurring.
- Mutually exclusive events: Events that cannot occur together.
- Exhaustive events: A set of events where one of the events must occur.
It also provides examples and introduces the classical definition of probability as the number of favorable outcomes divided by the total number of outcomes.
4.1-4.2 Sample Spaces and Probability
The document defines key concepts in probability theory, such as probability experiments, outcomes, sample spaces, events, classical probability, empirical probability, and subjective probability. It provides examples of how to calculate probabilities of simple and compound events using classical probability methods, including determining probabilities using fractions or decimals and interpreting "and" and "or" probabilities.
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This document discusses the concept of probability. It defines probability as a measure of how likely an event is to occur. Probabilities can be described using terms like certain, likely, unlikely, and impossible. Mathematically, probabilities are often expressed as fractions, with the numerator representing the number of possible outcomes for an event and the denominator representing the total number of possible outcomes. The document provides examples to illustrate concepts like independent and conditional probabilities, as well as complementary events and the gambler's fallacy.
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Probability
Probability is the chance that something will happen or the likelihood of an event. It is measured by the number of favorable outcomes divided by the total number of possible outcomes. Some key contributors to the development of probability include Buffon, Kerrich, and Pearson who performed coin toss experiments to determine experimental probabilities. Probability is used in various real-life domains like weather forecasting, insurance policies, sports strategies, and medical decisions.
probability
This document provides an overview of probability concepts including:
- Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
Basic probability Concepts and its application By Khubaib Raza
introduction of probability probability defination and its properties after that difference between probability and permutation in the last Discuss about imporatnace of Probabilty in Computer Science
Basic probability concept
This document outlines basic probability concepts, including definitions of probability, views of probability (objective and subjective), and elementary properties. It discusses calculating probabilities of events from data in tables, including unconditional/marginal probabilities, conditional probabilities, and joint probabilities. Rules of probability are presented, including the multiplicative rule that the joint probability of two events is equal to the product of the marginal probability of one event and the conditional probability of the other event given the first event. Examples are provided to illustrate key concepts.
Probability(mutually exclusive events)
The document contains solutions to 3 probability problems:
1) Finding the probability of rolling a die with a face that is a multiple of 3 or 5. The probability is 5/6.
2) Finding the probability that a randomly selected digit between 1-50 is a multiple of 10 or 11. The probability is 18/50.
3) Finding the probability that a randomly drawn card is a queen or king. The probability is 8/52.
Probability
The document provides an overview of key probability concepts including:
1. Random experiments, sample spaces, events, and the classification of events as simple, mutually exclusive, independent, and exhaustive.
2. The three main approaches to defining probability: classical, relative frequency, and subjective.
3. Important probability theorems like the addition rule, multiplication rule, and Bayes' theorem.
4. How to calculate probabilities of events using these theorems, including examples of finding probabilities of independent, dependent, mutually exclusive, and conditional events.
Complements and Conditional Probability, and Bayes' Theorem
๏บPlease Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.3: Complements and Conditional Probability, and Bayes' Theorem
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The document provides an introduction to probability. It discusses:
- What probability is and the definition of probability as a number between 0 and 1 that expresses the likelihood of an event occurring.
- A brief history of probability including its development in French society in the 1650s and key figures like James Bernoulli, Abraham De Moivre, and Pierre-Simon Laplace.
- Key terms used in probability like events, outcomes, sample space, theoretical probability, empirical probability, and subjective probability.
- The three types of probability: theoretical, empirical, and subjective probability.
- General probability rules including: the probability of impossible/certain events; the sum of all probabilities equaling 1; complements
mutually-exclusive-events.ppt
Mutually exclusive events cannot occur at the same time. The probability of event A or B occurring is calculated as P(A) + P(B). Independent events do not influence each other, so P(A and B) = P(A) ร P(B). Dependent events influence each other, so P(A and B) = P(A) ร P(B after A). Examples are provided to demonstrate calculating probabilities for mutually exclusive, independent, and dependent events.
Quartile in Statistics
The document discusses quartiles, which divide a data set into four equal parts. The first quartile contains the smallest 25% of values, the second quartile contains values between the 25th and 50th percentiles, the third quartile contains values between the 50th and 75th percentiles, and the fourth quartile contains the largest 25% of values. Formulas are provided for calculating the lower quartile (Q1), median (Q2), and upper quartile (Q3). The quartile deviation is defined as half the distance between Q3 and Q1, while the interquartile range is the full distance between Q3 and Q1. Examples are given to illustrate quartile calculations.
Introduction to Statistics and Probability
This document provides an introduction to statistics and probability. It discusses key concepts in descriptive statistics including measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and measures of shape (skewness, kurtosis). It also covers correlation analysis, regression analysis, and foundational probability topics such as sample spaces, events, independent and dependent events, and theorems like the addition rule, multiplication rule, and total probability theorem.
01_Probability of Simple Events.ppt
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This document explains how to create and interpret stem-and-leaf plots, which organize numeric data into place values to facilitate analysis. It provides examples of creating stem-and-leaf plots from sets of test scores and Olympic speed skating times. Key aspects covered include using stems for tens places and leaves for ones, adding a title and key, and how stem-and-leaf plots can be used to find the median, mode, and minimum/maximum values from a data set.
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Probability And Probability Distributions
This document provides an overview of key concepts in probability and probability distributions. It defines important terms like probability, sample space, events, mutually exclusive events, independent events, and conditional probability. It also covers rules of probability like addition rules, complement rules, and Bayes' theorem. Finally, it introduces discrete and continuous random variables and discusses properties of discrete probability distributions like expected value and standard deviation.
Introduction to Probability and Probability Distributions
This document provides an overview of teaching basic probability and probability distributions to tertiary level teachers. It introduces key concepts such as random experiments, sample spaces, events, assigning probabilities, conditional probability, independent events, and random variables. Examples are provided for each concept to illustrate the definitions and computations. The goal is to explain the necessary probability foundations for teachers to understand sampling distributions and assessing the reliability of statistical estimates from samples.
Probability
Probability is the measure of how likely something will occur.
It is the ratio of desired outcomes to total outcomes.
vinayjoshi-131204045346-phpapp02.pdf
This document provides an introduction to probability. It defines probability as a measure of how likely an event is to occur. Probability is expressed as a ratio of favorable outcomes to total possible outcomes. The key terms used in probability are defined, including event, outcome, sample space, and elementary events. The theoretical approach to probability is discussed, where probability is predicted without performing the experiment. Random experiments are described as those that may not produce the same outcome each time. Laws of probability are presented, such as a probability being between 0 and 1. Applications of probability in everyday life are mentioned, such as reliability testing of products. Two example probability problems are worked out.
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This document discusses types of probability and provides definitions and examples of key probability concepts. It begins with an introduction to probability theory and its applications. The document then defines terms like random experiments, sample spaces, events, favorable events, mutually exclusive events, and independent events. It describes three approaches to measuring probability: classical, frequency, and axiomatic. It concludes with theorems of probability and references.
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This document discusses exponential growth and decay functions. It provides examples of how to set up and solve exponential equations to model population growth, fish population decline, world poultry production increase, and bacterial growth. It also explains how to calculate half-life and doubling time for exponential decay and growth. Examples are worked through to find the half-life of tritium decaying at 5.471% per year and a radioactive substance decaying at 11% per minute, and to determine the amount of radioactive substance remaining after 6 years given its half-life is 3 years. The document concludes with assignments for students.
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Probability is the chance that something will happen or the likelihood of an event. It is measured by the number of favorable outcomes divided by the total number of possible outcomes. Some key contributors to the development of probability include Buffon, Kerrich, and Pearson who performed coin toss experiments to determine experimental probabilities. Probability is used in various real-life domains like weather forecasting, insurance policies, sports strategies, and medical decisions.
probability
This document provides an overview of probability concepts including:
- Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
Basic probability Concepts and its application By Khubaib Raza
introduction of probability probability defination and its properties after that difference between probability and permutation in the last Discuss about imporatnace of Probabilty in Computer Science
Basic probability concept
This document outlines basic probability concepts, including definitions of probability, views of probability (objective and subjective), and elementary properties. It discusses calculating probabilities of events from data in tables, including unconditional/marginal probabilities, conditional probabilities, and joint probabilities. Rules of probability are presented, including the multiplicative rule that the joint probability of two events is equal to the product of the marginal probability of one event and the conditional probability of the other event given the first event. Examples are provided to illustrate key concepts.
Probability(mutually exclusive events)
The document contains solutions to 3 probability problems:
1) Finding the probability of rolling a die with a face that is a multiple of 3 or 5. The probability is 5/6.
2) Finding the probability that a randomly selected digit between 1-50 is a multiple of 10 or 11. The probability is 18/50.
3) Finding the probability that a randomly drawn card is a queen or king. The probability is 8/52.
Probability
The document provides an overview of key probability concepts including:
1. Random experiments, sample spaces, events, and the classification of events as simple, mutually exclusive, independent, and exhaustive.
2. The three main approaches to defining probability: classical, relative frequency, and subjective.
3. Important probability theorems like the addition rule, multiplication rule, and Bayes' theorem.
4. How to calculate probabilities of events using these theorems, including examples of finding probabilities of independent, dependent, mutually exclusive, and conditional events.
Complements and Conditional Probability, and Bayes' Theorem
๏บPlease Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 4: Probability
4.3: Complements and Conditional Probability, and Bayes' Theorem
introduction to probability
The document provides an introduction to probability. It discusses:
- What probability is and the definition of probability as a number between 0 and 1 that expresses the likelihood of an event occurring.
- A brief history of probability including its development in French society in the 1650s and key figures like James Bernoulli, Abraham De Moivre, and Pierre-Simon Laplace.
- Key terms used in probability like events, outcomes, sample space, theoretical probability, empirical probability, and subjective probability.
- The three types of probability: theoretical, empirical, and subjective probability.
- General probability rules including: the probability of impossible/certain events; the sum of all probabilities equaling 1; complements
mutually-exclusive-events.ppt
Mutually exclusive events cannot occur at the same time. The probability of event A or B occurring is calculated as P(A) + P(B). Independent events do not influence each other, so P(A and B) = P(A) ร P(B). Dependent events influence each other, so P(A and B) = P(A) ร P(B after A). Examples are provided to demonstrate calculating probabilities for mutually exclusive, independent, and dependent events.
Quartile in Statistics
The document discusses quartiles, which divide a data set into four equal parts. The first quartile contains the smallest 25% of values, the second quartile contains values between the 25th and 50th percentiles, the third quartile contains values between the 50th and 75th percentiles, and the fourth quartile contains the largest 25% of values. Formulas are provided for calculating the lower quartile (Q1), median (Q2), and upper quartile (Q3). The quartile deviation is defined as half the distance between Q3 and Q1, while the interquartile range is the full distance between Q3 and Q1. Examples are given to illustrate quartile calculations.
Introduction to Statistics and Probability
This document provides an introduction to statistics and probability. It discusses key concepts in descriptive statistics including measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and measures of shape (skewness, kurtosis). It also covers correlation analysis, regression analysis, and foundational probability topics such as sample spaces, events, independent and dependent events, and theorems like the addition rule, multiplication rule, and total probability theorem.
01_Probability of Simple Events.ppt
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Stem and-leaf plots
This document explains how to create and interpret stem-and-leaf plots, which organize numeric data into place values to facilitate analysis. It provides examples of creating stem-and-leaf plots from sets of test scores and Olympic speed skating times. Key aspects covered include using stems for tens places and leaves for ones, adding a title and key, and how stem-and-leaf plots can be used to find the median, mode, and minimum/maximum values from a data set.
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The document discusses computing the mean, variance, and standard deviation of discrete random variables. It provides examples of calculating the mean of different probability distributions by taking the sum of each value multiplied by its probability. It also gives examples of finding variance by taking the sum of the squared differences between each value and the mean multiplied by its probability, and defines standard deviation as the square root of variance. The document aims to help readers understand how to calculate and interpret these statistical measures for discrete random variables.
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Probability
Probability is the measure of how likely something will occur.
It is the ratio of desired outcomes to total outcomes.
vinayjoshi-131204045346-phpapp02.pdf
This document provides an introduction to probability. It defines probability as a measure of how likely an event is to occur. Probability is expressed as a ratio of favorable outcomes to total possible outcomes. The key terms used in probability are defined, including event, outcome, sample space, and elementary events. The theoretical approach to probability is discussed, where probability is predicted without performing the experiment. Random experiments are described as those that may not produce the same outcome each time. Laws of probability are presented, such as a probability being between 0 and 1. Applications of probability in everyday life are mentioned, such as reliability testing of products. Two example probability problems are worked out.
Rishabh sehrawat probability
The document provides an introduction to probability. It defines probability as a measure of how likely an event is. Probability is expressed as the ratio of favorable outcomes to total possible outcomes. The concept of probability originated in the 16th century and has been developed by many mathematicians. Today, probability theory has applications in fields like science, economics, and engineering. The document also defines key probability terms like events, outcomes, sample space, and theoretical probability. It provides examples of calculating probability for experiments like tossing coins, rolling dice, and drawing cards.
Probability
Probability is a branch of mathematics that studies patterns of chance. It is used to quantify the likelihood of events occurring in experiments or other situations involving uncertainty. The probability of an event is expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty. Key concepts in probability include theoretical and experimental probability, sample spaces, events, mutually exclusive and exhaustive events, and rules like addition rules for calculating combined probabilities. Probability is applied in many fields including statistics, gambling, science, and machine learning.
probability-120904030152-phpapp01.pdf
Probability is a branch of mathematics used to quantify the likelihood of events occurring based on patterns of chance observed in experiments. It is defined as the ratio of favorable outcomes to total possible outcomes. Common probability terms include experiment, outcome, equally likely outcomes, sample space, event, and sample point. Probability calculations follow set rules and can be applied in various domains like gambling, science, and artificial intelligence.
PROBABILITY.pptx
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
PROBABILITY BY ZOEN CUTE KAAYO SA KATANAN.pptx
Probability is a branch of mathematics that enables us to predict the occurrence of an event as a result of an experiment. The probability of an event is calculated by taking the number of outcomes in the event and dividing it by the total number of possible outcomes. Simple events consist of a single outcome, while compound events consist of two or more simple events. Examples of calculating probability are given for simple events like rolling a die or drawing balls from a jar, and compound events like rolling two dice. The importance of probability in decision making in real life is discussed.
Mathematics
The document provides guidance on teaching a lesson on probability. It outlines key concepts to define, such as experimental and theoretical probabilities. It also describes solving problems involving combined probabilities of mutually exclusive and independent events. Example problems are provided for different probability concepts. The teacher is instructed to check students' understanding through oral questions and exercises.
Probablity ppt maths
The document provides an overview of probability concepts including:
- Probability is a measure of how likely an event is, defined as the number of favorable outcomes divided by the total number of possible outcomes.
- Theoretical probability predicts outcomes without performing experiments, dealing with events as combinations of elementary outcomes.
- Random experiments may have different results each time while deterministic experiments always produce the same outcome.
- Elementary events are individual outcomes, and compound events combine multiple elementary outcomes.
- Theoretical probability of an event is the number of favorable elementary events divided by the total number of possible events.
- The probabilities of an event and its negation must sum to 1.
PROBABILITY
This is benefical for student mainly for class 10. And the ppt material is extracted from R.D. Sharma and 10 NCERT Text book.
EVENTS AND TYPES OF EVENTS
This document defines different types of events in probability and provides examples. It discusses impossible and sure events, simple events which consist of a single outcome, and compound events which consist of multiple outcomes. It also covers independent events which are unaffected by other events, dependent events which are affected by others, and mutually exclusive events which do not share any common outcomes. Finally, it defines exhaustive events as a set that covers the entire sample space and provides two examples to illustrate these concepts.
Skill20 probability
Probability can be expressed as a fraction, decimal, or percentage to represent the likelihood of an event occurring. Simple probability problems involve single events like rolling a die or flipping a coin, where the probability is calculated by the number of successful outcomes divided by the total number of possible outcomes. More complex probability questions deal with compound events that require multiple steps, like rolling a die and flipping a coin, where the probabilities of each step must be multiplied. Probability problems can also involve dependent events where items are drawn from a collection with or without replacement.
Probability..
This document discusses key concepts in probability, including:
1) Probability is a measure of likelihood that an event will occur in a random experiment, where the outcome cannot be predicted with certainty. The sample space is the set of all possible outcomes.
2) Random variables assign a numerical value to each outcome. Discrete variables use counting, while continuous variables use measuring.
3) Theoretical probability is based on reasoning about what should happen, while experimental probability is based on experimental results.
4) Equally likely events have the same probability of occurring. Complementary events are all possible outcomes besides the given event. Independent events do not affect each other's probabilities.
probability-120611030603-phpapp02.pptx
This document provides an overview of key probability concepts including:
- Random experiments, outcomes, events, sample spaces, mutually exclusive and independent events
- Classical, relative frequency, subjective, and axiomatic approaches to defining probability
- Probability theorems including addition, multiplication, Bayes' theorem, and their applications to dependent and independent events
- Examples are provided to illustrate concepts like conditional probability and using Bayes' theorem to update probabilities with new information
Probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event.
S1 sp
This document provides an introduction to probability and some key probability concepts. It discusses how probability can be used to measure the chance of outcomes in random experiments and defines key terms like sample space, events, equally likely events, unions and intersections of events. It also presents the classical approach to defining probability mathematically as the ratio of favorable outcomes to total possible outcomes when conditions like equally likely outcomes are met. Several examples are provided to illustrate probability calculations.
Probability presentation
This document defines key concepts in probability, including:
- Probability is the chance or likelihood of an event occurring.
- Random experiments are those with unpredictable outcomes.
- The sample space is the set of all possible outcomes of an experiment.
- Events are subsets of the sample space. Simple events have one outcome, compound events have multiple.
- Equally likely events have no greater or lesser chance of occurring.
- Mutually exclusive events cannot occur simultaneously.
- Exhaustive and mutually exclusive events partition the sample space, with no overlap between events.
- Probability is calculated by dividing the number of favorable outcomes by the total number of outcomes.
01_Probability of Simple Events.ppt
This document discusses probability of simple events. It defines key terms like outcome, sample space, simple event and complementary events. It provides examples of calculating probability for events like rolling dice, spinning a spinner or flipping a coin. The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes. Students are given examples to practice calculating probabilities and real world scenarios are provided to demonstrate applications of probability.
Making probability easy!!!
This presentation is about the topic PROBABILITY. Details of this topic, starting from basic level and slowly moving towards advanced level , has been discussed in this presentation.
01_Probability-of-Simple-Events-Math.ppt
This document provides instruction on probability of simple events. It defines key terms like outcome, sample space, simple event and complementary events. Examples are given to demonstrate calculating probability as the number of favorable outcomes over total possible outcomes, such as the probability of rolling a 4 on a die or flipping a tail. Practice problems have students calculate probabilities of independent events like drawing a red card. The document concludes with a real-world example of calculating the probability a purchased computer is not defective.
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TYPES OF EVENTS.pdf
- 1. Probability - Type of events ?? 4 12 4 12 5.76 53% 53% 0.3425 53% 7.802
- 2. Lesson Outline Here's an overview of today's lesson. Probability Determining the probability Types of events 3 15 0.645 74% 26% 0.3425
- 3. What is it? Probability refers to the chance or possibility that an event will occur. It is the ratio of the number of desired outcomes to the total number of outcomes. Probability = number of desired outcomes total number of outcomes Probability ranges from 0 to 1. 0 impossible to occur event will surely happen 1 ?? 7 14 3.549 38% 56% 0.3425 6 48
- 4. Probability = number of desired outcomes total number of outcomes ?? Probability = 1 only 1 marble is blue total number of marbles is 5 5 There are 5 colored marbles in a box. What is the probability of randomly picking a blue marble? Determining the Probability
- 5. Determining the Probability There are 5 colored marbles in a box. What is the probability of randomly picking a green marble? Probability = number of desired outcomes total number of outcomes Probability = there are 3 green marbles that can be picked from the box total number of marbles is 5 3 5
- 6. Determining the Probability There are 5 colored marbles in a box. What is the probability of randomly picking a black marble? Probability = number of desired outcomes total number of outcomes Probability = there are no black marbles in the box total number of marbles is 5 0 5 Probability = 0 It is impossible to pick black marbles.
- 7. 4 24 Sure event Impossible event Complementary event Mutually exclusive event Mutually inclusive event Exhaustive event Equally likely event TYPES OF EVENTS 0.6281 37% 32% 6.392
- 8. SURE EVENT A sure event is one that will always happen. The probability of occurrence of a sure event will always be 1. Example:the earth revolving around the sun is a sure event.
- 9. IMPOSSIBLE EVENT If the probability of occurrence of an event is zero, then it is an impossible event. Example: The event of getting 7 when a die is thrown is impossible. This is because the outcomes of the throwing a die include {1, 2, 3, 4, 5, 6}.
- 10. COMPLEMENTARY EVENT For every event A, there corresponds another event A is called the complementary event to A. It is also called the event โnot Aโ. For example, on tossing a coin let E be defined as getting a head. Then the complement of E is E' which will be the event of getting a tail. Thus, E and E' together make up complementary events.
- 11. MUTUALLY EXCLUSIVE EVENTS Events that cannot occur at the same time are known as mutually exclusive events. Thus, mutually exclusive events in probability do not have any common outcomes. Example :When we roll a die, the sample space S = {1,2,3,4,5,6}. (i) Since{1, 3} {2, 4, 5, 6}= , โฉ โ t he events {1,3}and{2, 4,5,6}are mutually exclusive events.
- 12. MUTUALLY INCLUSIVE EVENTS Two events are mutually inclusive when they can both occur simultaneously. Example :When we roll a die, the sample space S = {1,2,3,4,5,6}. (i) The events {2,3,5},{5,6} are mutually inclusive, since {2, 3, 5} {5, 6}= 5 โฉ โ โ
- 13. EXHAUSTIVE EVENTS A set of events is called exhaustive if all the events together consume the entire sample space. In other words, a set of events out of which at least one is sure to occur when the experiment is performed are exhaustive events. Example : the outcome of an exam is either passing or failing.
- 14. EQUALLY LIKELY EVENTS Equally likely events in probability are those events in which the outcomes are equally possible. For example, on tossing a coin, getting a head or getting a tail, are equally likely events.
- 15. ?? 3 10 5 15 Let's try: A number from 1 to 25 is drawn at random. What is the probability of getting a number greater than 13? 0.645 64% 32% 0.3425 0.9785
- 16. 12 25 Here's the answer :