Probability
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Probability is a measure of how likely an event is to occur. It is expressed as a fraction between 0 and 1, where the numerator is the number of favorable outcomes and the denominator is the total number of possible outcomes. There are general rules for probability - the probabilities of all outcomes must sum to 1, and the probability of an event not occurring is 1 minus the probability of it occurring. Probability is used in many fields involving chance, like math, statistics, finance, science, and more.
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Probability is a mathematical measure of how likely events are to occur. It can be expressed as a fraction, decimal, or percentage between 0 and 1. A probability experiment involves possible outcomes that make up a sample space. An event is a subset of outcomes. Theoretical probability calculates the likelihood of an event based on equally likely outcomes. Experimental probability is based on observed frequencies. Subjective probability relies on estimates rather than calculations. As experiments are repeated, experimental probability approaches theoretical probability due to the law of large numbers.
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.
Theoretical Probability
The document discusses theoretical probability and how to calculate it. Theoretical probability is estimated when all outcomes are equally likely, and is calculated by taking the number of ways the event can occur divided by the total number of possible outcomes. Two examples are provided: the probability of a fair coin landing heads is 1/2, and the probability of rolling less than 5 on a fair die is 4/6. The document also explains that the probability of an event not occurring is 100% minus the probability of the event occurring.
PROBABILITY BY SHUBHAM
This document discusses key concepts of probability, including experimental probability, theoretical probability, outcomes, events, sample space, impossible events, sure events, equally likely events, and mutually exclusive events. It provides examples to illustrate experimental probability, which is calculated based on results of repeated experiments, and theoretical probability, which is calculated based on the number of possible outcomes. The document aims to help readers understand the different types of probability and how to distinguish between experimental and theoretical probability.
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
This document defines and explains key concepts related to probability. It begins by defining probability as "the way of expressing knowledge of belief that an event will occur on chance." It then provides definitions of theoretical probability as the number of favorable outcomes divided by the total number of outcomes, and experimental probability as the ratio of times an event occurred to the total number of trials. The document outlines common probability terms like sample space, events, outcomes, and exhaustive events. It also lists some general rules of probability like the sum of all probabilities equals 1 and the probability of an impossible event is 0. In closing, it notes that probability is used in many fields like math, statistics, finance, science, and artificial intelligence.
Chapter – 15 probability maths || CLASS 9 || The World Of presentation youtub...
This document defines probability and provides examples of calculating probability through experiments involving coin tossing and dice rolling. It states that probability is a measure between 0 and 1 of the likelihood of an event occurring, with 0 being impossible and 1 being certain. The basic probability formula is defined as the number of favorable outcomes divided by the total number of possible outcomes. Experiments are defined as procedures that can be repeated with a set of possible outcomes, with each repetition being a trial. The probability of an event is calculated by taking the number of outcomes where the event occurs and dividing by the total number of outcomes.
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Probability is a mathematical measure of how likely events are to occur. It can be expressed as a fraction, decimal, or percentage between 0 and 1. A probability experiment involves possible outcomes that make up a sample space. An event is a subset of outcomes. Theoretical probability calculates the likelihood of an event based on equally likely outcomes. Experimental probability is based on observed frequencies. Subjective probability relies on estimates rather than calculations. As experiments are repeated, experimental probability approaches theoretical probability due to the law of large numbers.
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.
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The document discusses theoretical probability and how to calculate it. Theoretical probability is estimated when all outcomes are equally likely, and is calculated by taking the number of ways the event can occur divided by the total number of possible outcomes. Two examples are provided: the probability of a fair coin landing heads is 1/2, and the probability of rolling less than 5 on a fair die is 4/6. The document also explains that the probability of an event not occurring is 100% minus the probability of the event occurring.
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This document discusses key concepts of probability, including experimental probability, theoretical probability, outcomes, events, sample space, impossible events, sure events, equally likely events, and mutually exclusive events. It provides examples to illustrate experimental probability, which is calculated based on results of repeated experiments, and theoretical probability, which is calculated based on the number of possible outcomes. The document aims to help readers understand the different types of probability and how to distinguish between experimental and theoretical probability.
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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
This document defines and explains key concepts related to probability. It begins by defining probability as "the way of expressing knowledge of belief that an event will occur on chance." It then provides definitions of theoretical probability as the number of favorable outcomes divided by the total number of outcomes, and experimental probability as the ratio of times an event occurred to the total number of trials. The document outlines common probability terms like sample space, events, outcomes, and exhaustive events. It also lists some general rules of probability like the sum of all probabilities equals 1 and the probability of an impossible event is 0. In closing, it notes that probability is used in many fields like math, statistics, finance, science, and artificial intelligence.
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This document defines probability and provides examples of calculating probability through experiments involving coin tossing and dice rolling. It states that probability is a measure between 0 and 1 of the likelihood of an event occurring, with 0 being impossible and 1 being certain. The basic probability formula is defined as the number of favorable outcomes divided by the total number of possible outcomes. Experiments are defined as procedures that can be repeated with a set of possible outcomes, with each repetition being a trial. The probability of an event is calculated by taking the number of outcomes where the event occurs and dividing by the total number of outcomes.
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Probability
Probability is a measure of how likely outcomes of uncertain events are to occur. It can be determined through experiments repeated over the long-term to reveal consistent patterns (the classical method), by observing the proportion of outcomes in many trials of an experiment (the empirical method), or based on subjective judgments of likelihood (the subjective method). The probability of any given event is calculated as the number of desired outcomes divided by the total number of possible outcomes, assuming all outcomes are equally likely.
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Probability is a branch of mathematics that studies patterns of chance and uncertainty. It is expressed as a number between 0 and 1 that indicates how likely an event is to occur based on the number of possible outcomes. For example, the probability of flipping a coin and getting heads is 1/2 or 50% since there are two possible outcomes and one favors heads. Probability can be theoretical, based on the number of outcomes, or experimental, based on recording results of repeated trials. Key terms include experiment, outcome, sample space, event, and probability definitions for single and multiple events.
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The document is a presentation on probability that discusses:
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2) Examples of describing probability using terms like certain, likely, unlikely, and impossible.
3) Examples of calculating probability using a dice and coin toss, with the dice example having a 1/6 probability of rolling any single number and the coin toss a 1/2 probability of getting heads.
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The document is a presentation about probability that contains the following key points:
1) It defines probability as a fraction where the numerator is the number of possible ways an event can occur and the denominator is the total number of possible events.
2) It describes how probabilities can be expressed as terms like certain, likely, unlikely, and impossible.
3) It provides examples of calculating probabilities using a dice and coin toss. The probability of rolling a specific number on a six-sided dice is 1/6 and the probability of heads or tails when tossing a coin is 1/2.
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Experimental probability is calculated by performing an experiment and recording the outcomes, while theoretical probability can be calculated without performing an experiment based on the possible outcomes. As the number of trials in an experiment increases, the experimental probability gets closer to the theoretical probability due to the Law of Large Numbers. Some examples are given of calculating experimental and theoretical probabilities for coin tosses and drawing marbles from a bag.
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The document defines probability as a measure of how likely an event is to occur, expressed as a ratio from 0 to 1. It discusses the basics of probability formulas and the three main types: theoretical, experimental, and axiomatic probability. Theoretical probability uses the ratio of favorable to total outcomes without experiments. Experimental probability is based on conducting actual experiments and recording results. Axiomatic probability sets axioms that apply to all probability types, including Kolmogorov's three axioms that define probability as a positive real number between 0 and 1.
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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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Probability is the mathematics of chance that can be expressed as a fraction, decimal, or percentage. It provides the likelihood that a given event will occur based on the number of possible outcomes of an experiment. The probability of any single event must be between 0 and 1, and the sum of probabilities of all events must equal 1. Common experiments used to demonstrate probability include tossing a coin, rolling a die, and tossing two coins simultaneously, with the outcomes and events defined for each. The theoretical probability of an event is calculated by dividing the number of outcomes for that event by the total number of possible outcomes.
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Probability refers to the likelihood of an event occurring, expressed as a value between 0 and 1. It is a branch of mathematics used to predict the chance of future events. There are different types of probability distributions that describe the chances of various outcomes in random experiments or events, such as the binomial, normal, and uniform distributions. Probability and statistics are related but distinct concepts, with probability focusing on chances and statistics handling the analysis of data.
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The document discusses the history and concepts of probability. It outlines that probability theory originated from a gambling dispute in the 17th century and developed rapidly in the 18th century. It defines probability as a number between 0 and 1 that reflects the likelihood of an event occurring. It also classifies the different types of probabilities as theoretical, experimental, and axiomatic probability and provides examples of where probability is used in real life situations and how it can help develop critical thinking skills.
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Probability is the likelihood that an event will occur, calculated by dividing the number of favorable outcomes by the total possible outcomes. It is used to make decisions when outcomes are uncertain. The document discusses theoretical, experimental, and axiomatic probability, and provides examples of calculating theoretical probability by dividing the number of favorable outcomes by total outcomes.
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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The document is a presentation about probability that contains the following key points:
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Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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Probability
- 1. Probability
- 2. What is Probability?•Probability is the measure of how likely an event or outcome is. •Different events have different probabilities! Definition Of Theoretical Probability P(E)= No. of Favorable outcomes Total no. of outcomes Where E = event
- 3. How do we express Probabilities? Usually, we express probabilities as fractions. 1. The numerator shows the POSSIBLE number of ways an event can occur. 2. The denominator is the TOTAL number of possible events that could occur.
- 4. Some common terms related to Probability Experiment: It is a situation involving chance or probability that leads to results called outcomes. Event: Number of outcomes in an experiment. Outcome: A possible result of a random experiment.
- 5. Probability- General Rules 1. Probability is a number between 0 and 1. 2. The sum of the probabilities of all possible outcomes in a sample space is 1. 3. The probability that an event does not occur is 1 minus the probability that it does occur. (also called the complement of A) P(not E) = 1- P(E)
- 6. For example The chance of a coin landing on heads is 50%. This is because a coin has two sides so there is a 50% chance that the coin will land on heads and 50% that a coin will land on tails.
- 7. Where is Probability Used? Probability is used a lot in daily life, Probability is used in such as Math, Statistics, Finance, Gambling, Science, Machine and Artificial Intelligence, and in many other activities.
- 8. When question arises related to chance of something happening , you are dealing with probability.
- 9. In this bag of marbles, there are: 3 red marbles 2 white marbles 1 purple marble 4 green marbles
- 10. 1. How many red marbles are in the bag? Solution:-3/10 or 0.3 2. How many Green marbles are there in the bag? Solution:-4/10 = 2/5 or 0.4
- 11. Thank You