Theoretical overview of probability and types.pptx
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This document provides an overview of probability and its types. It introduces probability as dealing with random events and outlines the formula for calculating probability. It then describes the main types as theoretical probability based on possible chances, experimental probability based on observed experiments, and axiomatic probability which uses a set of rules. The document also defines some key probability events like equally likely, complementary, impossible, and mutually exclusive events. It concludes by listing some common applications of probability such as weather, sports, insurance, and games.
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Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.[note 1][1][2] The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ('heads' and 'tails') are both equally probable; the probability of 'heads' equals the probability of 'tails'; and since no other outcomes are possible, the probability of either 'heads' or 'tails' is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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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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The document provides an introduction to probability theory, including definitions of key terms like trial, event, exhaustive events, favorable events, independent events, mutually exclusive events, and equally likely events. It discusses three approaches to defining probability: classical, statistical, and axiomatic. The classical approach defines probability as the ratio of favorable cases to total possible cases. The statistical approach determines probabilities based on empirical observations over many trials. The axiomatic approach uses set theory and axioms to define probability without restrictions of previous approaches.
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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.
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This document provides an overview of probability theory concepts. It defines an experiment as any process of observation or measurement, and a random experiment as one where the exact outcome cannot be predicted but the possible outcomes can be listed. The sample space is the set of all possible outcomes, and a subset is called an event. Probability is defined as the ratio of favorable outcomes to total possible outcomes. Examples are provided of calculating probabilities of events occurring for experiments like rolling dice, tossing coins, and assigning student grades.
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Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.[note 1][1][2] The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ('heads' and 'tails') are both equally probable; the probability of 'heads' equals the probability of 'tails'; and since no other outcomes are possible, the probability of either 'heads' or 'tails' is 1/2 (which could also be written as 0.5 or 50%).
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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.
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Prokaryotic DNA replication begins at the origin of replication and proceeds bidirectionally. It involves three main steps: initiation, elongation, and termination. Initiation begins at the origin of replication site, where proteins bind and unwind the DNA. Elongation then uses DNA polymerase III to simultaneously synthesize the leading and lagging strands. Termination occurs when the replication forks from opposite directions meet at the termination site and halt, resolving issues through proteins like TUS and topoisomerases.
Prokaryotic DNA replication.pptx
Prokaryotic DNA replication begins at the origin of replication site where the replication fork is formed. DnaA and other proteins recognize the origin site and unwind the DNA double helix. RNA primers are synthesized which allows DNA polymerase III to begin bidirectional DNA synthesis of the leading and lagging strands. Okazaki fragments are formed and ligated on the lagging strand. Replication terminates when the replication forks meet at the termination site and the daughter chromosomes are separated.
DNA repair mechanism and their types.pptx
DNA repair is a collection of processes cells use to identify and correct damage to DNA. There are several types of DNA repair mechanisms, including direct repair, base excision repair, mismatch repair, recombination repair, and SOS repair. DNA repair has advantages of maintaining genetic integrity between generations and preserving individual health, but defects can lead to increased cancer risks and premature aging syndromes.
TOPIC NAME Structure of DNA and their Type.pptx
DNA has a double helix structure that resembles a twisted ladder. It is composed of nucleotides, each containing a sugar, phosphate group, and one of four nitrogen bases (A, T, C, or G). The bases on opposite strands bond together via hydrogen bonds between A-T and C-G to form the structure. Erwin Chargaff discovered that the amounts of A and T are equal, as are the amounts of C and G in any DNA sample. There are three types of DNA structures: A-DNA, B-DNA, and Z-DNA.
LAC OPERON SYSTEM.pptx
The document describes the lac operon system, which was the first operon described in 1961 and controls the catabolism of lactose in prokaryotes. The lac operon has 5 structural units - a promoter, operator, three structural genes (LacZ, LacY, LacA) that encode enzymes for lactose breakdown, CAP binding sites, and a regulatory gene. When lactose is absent, a repressor protein binds to the operator, preventing transcription of the structural genes. When lactose is present, it binds to the repressor and causes a conformational change that releases it from the operator, allowing transcription and the breakdown of lactose.
LAC OPERON 2.pptx
The lac operon is a cluster of three genes in prokaryotes that are involved in processing the sugar lactose. It consists of a promoter, operator, and structural genes. The lac operon is inducible, meaning it is only transcribed when lactose is present. Depending on whether lactose and glucose are present or absent, the lac operon will be either actively transcribed or transcriptionally inactive.
DNA STRUCTURE AND TYPES.pptx
DNA is a double-stranded molecule composed of nucleotides that contain nitrogenous bases, a deoxyribose sugar, and a phosphate group. The bases--cytosine, thymine, adenine, and guanine--form rungs of a twisted ladder structure, while the alternating sugar and phosphate molecules form the sides. Watson and Crick discovered that the bases pair up specifically through hydrogen bonds to form the DNA double helix, which contains the genetic information needed to build an organism. DNA can take on different secondary structures including A-DNA, B-DNA, and Z-DNA forms.
TOPIC-DNA repair mechanism and their types.pptx
DNA repair mechanisms are necessary to correct damage to DNA that could otherwise lead to mutations and cancer. There are several types of DNA repair mechanisms that address different types of damage, including base repair through excision, resynthesis and ligation of bases, nucleotide excision repair to address mismatches, and mismatch repair to fix errors. Double stranded breaks can be repaired through non-homologous end joining or homologous recombination repair.
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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
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- 1. Theoretical overview of probability and types
- 2. Introduction :- Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
- 3. Formula :- Probability of event to happen P(E) = Number of favorable outcomes Total Number of outcomes Example :- 1) There are 6 pillows in a bed, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a yellow pillow? Ans: The probability is equal to the number of yellow pillows in the bed divided by the total number of pillows, i.e. 2/6 = 1/3.
- 4. Types :- Theoretical Probability : It is based on the possible chances of something to happen. Experimental Probability : It is based on the basis of the observations of an experiment. Axiomatic Probability : In axiomatic probability, a set of rules or axioms are set, which applies to all types
- 5. events : 1) Equally likely events Equally likely events in probability are those events in which the outcomes are equally possible. 2) Complementary events When there are two events such that one event can occur if and only if the other does not take place then such events are known as complementary events. 3) Impossible events An event that can never happen is known as an impossible event. 4) Mutually exclusive events Events that cannot occur at the same time are known as mutually exclusive events.
- 6. Applications :- Weather Sports Insurance Games
- 7. THANK YOU